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Vol.  XXX 
N«.  6 


PSYCHOLOGICAL  REVIEW  PUBLICATIONS 


Wkole  No.  139 
1921 


THE 

Psychological  Monographs 

EDITED  BY 

JAMES  ROWLAND  ANGELL,  Yale  University 
HOWARD  C.  WARREN,  Princeton  University  ( Review ) 

JOHN  B.  WATSON,  New  York  (7.  of  Exp.  Psychol.) 

SHEPHERD  I.  FRANZ,  Govt.  Hosp.  for  Insane  ( Bulletin )  and 
MADISON  BENTLEY,  University  of  Illinois  (Index) 


The  Interrelation  of  Some  Higher 

Learning  Processes 

I 

BY 

V 

B.  F.  HAUGHT,  Ph.D. 

Associate  Professor  of  Psychology,  State  University  of  New  Mexico 


PSYCHOLOGICAL  REVIEW  COMPANY 

PRINCETON,  N.  J. 
and  LANCASTER,  PA. 


Agents:  G.  E.  STECHERT  &  CO.,  London  (2  Star  Yard,  Carey  St.,  W.C.) 

Paris  (16  rue  de  Conde) 


FOREWORD 


The  writer  is  greatly  indebted  to  Dr.  Joseph  Peterson  whose 
guidance  and  personal  interest  have  been  of  inestimable  value 
throughout  the  conduct  of  this  investigation  and  whose  scientific 
attitude  has  been  a  source  of  great  inspiration.  He  also  wishes 
to  take  this  opportunity  to  express  his  thanks  and  appreciation 
to  the  students  who  served  patiently  as  subjects  to  make  the 
investigation  possible,  and  especially  to  his  wife  who  assisted 
greatly  in  making  the  mathematical  calculations. 


ERRATA 

Attention  is  directed  to  the  following  list  of  corrections  of  er¬ 
rors,  which  unfortunately  were  not  remarked  in  time  to  be  set 
right  in  the  body  of  the  text : 

In  Table  VIII,  p.  21,  “100-19,"  lower  left  corner,  should  read 
“0-19.”  “50-64"  in  top  row  should  read  “60-64.” 

In  Table  X,  p.  23,  “0-10”  in  top  row  should  read  “0-19." 

In  Table  XV,  p.  31,  the  omitted  spaces  in  the  base  line  should 
be  6  and  8,  respectively,  from  left  to  right;  and  “20-25”  in  the 
top  row  should  read  “20-24." 

In  Table  XVI,  p.  32,  “(Modified)”  should  be  added  at  the  end 
of  the  line  just  over  the  figure,  beginning  “X  =  .” 

In  Table  XVII,  p.  33,  numbers  omitted  in  lower  row  should  be, 
from  left  to  right :  3,  2,  3,  5,  7,  8,  9,  9,  7,  6,  7,  3,  3,  and  2. 

In  Table  XXII,  p.  41,  “54-60"  in  first  column  should  read 
“64-60;"  and  “35-35  in  the  top  row  should  read  “35-39.” 

In  Table  XXV,  p.  47,  7  and  17  in  the  9th  and  the  10th  squares 
of  the  bottom  row  should  be  11  and  13,  respectively. 


TABLE  OF  CONTENTS 


SECTION  PAGE 

I.  The  Problem .  i 

II.  The  Method  .  2 

1.  Scores  reduced  to  percentiles  .  2 

2.  Selection  of  a  criterion  .  3 

3.  Scoring  tests  in  the  light  of  the  criterion .  6 

III.  Subjects .  8 

1.  Manner  of  selecting  .  8 

2.  College  class  and  social  status  . . .  8 

IV.  The  Binet-Simon  Tests  .  8 

1.  Order  of  giving  tests  .  8 

2.  Method  of  finding  intelligence  quotient .  10 

V.  The  Rational  Learning  Test  .  11 

1.  Description  of  test  .  11 

2.  Method  of  scoring .  14 

3.  Analysis  of  data  .  18 

VI.  Rational  Learning  (Modified)  .  23 

1.  Description  of  test  .  23 

2.  Method  of  scoring  .  25 

3.  Analysis  of  data  .  28 

VII.  The  Checker  Puzzle  Test .  34 

1.  Description  of  test  .  . . .  34 

2.  Method  of  scoring .  36 

3.  Analysis  of  data . 36 

VIII.  The  Tait  Labyrinth  Puzzle .  37 

1.  Description  of  test  . 37 

2.  Method  of  scoring .  38 

3.  Analysis  of  data .  38 


v 


VI 


TABLE  OF  CONTENTS 


SECTION  PAGE 

IX.  Intercorrelations  .  40 

1.  Tests  analyzed  by  comparison  with  the  criterion  40 

a.  Rational  learning  analyzed  .  42 

b.  Rational  learning  (modified)  analyzed  ...  43 

c.  Checker  puzzle  test  analyzed  .  46 

d.  Tait  labyrinth  puzzle  analyzed  .  48 

2.  Intercorrelations  of  tests  scored  in  the  light  of 

the  criterion  .  49 

3.  Intercorrelation  of  tests  scored  by  combining  the 

factors  equally  .  54 

X.  Discussion  of  Learning  and  Intelligence .  58 

1.  Spearman's  two  factor  theory  .  59 

2.  The  multiple  factor  theory .  62 

XI.  Summary  and  Conclusions .  .  65 

1.  Method  .  65 

2.  Results  .  67 

Bibliography  .  70 


THE  INTERRELATION  OF  SOME  HIGHER 
LEARNING  PROCESSES 


I.  Problem 

The  purpose  of  this  investigation  is  to  analyze  and  to  study 
the  interrelations  of  some  higher  mental  processes.  Each  of  the 
experiments  used  involves  two  or  more  factors,1  such  as  time, 
repetitions,  solutions,  errors,  etc.  Each  problem  requires  con¬ 
siderable  time  for  the  learning  and  in  this  respect  is  different 
from  the  individual  parts  of  most  intelligence  tests.  The  pro¬ 
blems  are  also  of  such  a  nature  that  the  subject  may  solve  them 
either  by  the  hit-and-miss  method  or  by  a  reflective  method.  In 
every  case  it  is  possible  to  record  all  the  responses  of  the  subject, 
and  thus  provide  objective  data  for  the  analysis. 

The  purpose  is  to  compare  each  factor  in  the  tests  with  a 
criterion  and  with  every  other  factor.  The  tests  will  be  scored 
by  combining  the  significant  factors  and  they  will  then  be  further 
compared  with  the  criterion  and  with  each  other.  In  this  way  it 
is  believed  that  a  detailed  analysis  can  be  made  that  will  throw 
light  on  methods  of  learning  and  on  the  characteristics  of  tests 
involving  the  higher  mental  processes.  This  procedure  will 
analyze  not  only  the  tests  used,  but  also  the  criterion.  An 
attempt  will  be  made  to  answer  such  questions  as  the  following : 
Does  time  measure  any  elements  in  learning  that  are  not  meas¬ 
ured  by  the  criterion  ?  Does  time  measure  any  elements  in  learn¬ 
ing  that  are  not  measured  by  repetitions  or  errors?  Does  one 
rational  learning  experiment  involve  the  same  functions  as  any 
other?  Is  there  a  general  rational  learning  function,  or  are  such 
types  of  learning  simply  operations  of  various  factors  in  different 
sorts  of  combinations. 

1  Factor  is  used  in  this  investigation  to  designate  one  kind  of  data,  such  as 
time,  repetitions,  solutions,  errors,  etc. 


2 


B.  F.  H AUGHT 


II.  Method 

The  raw  scores  in  each  experiment  are  first  put  into  percentiles 
by  use  of  Rugg’s  table.2  In  order  to  shorten  the  work  a  table 
based  on  seventy-four  cases,  the  number  used  in  this  investiga¬ 
tion,  was  constructed.  Three  steps  are  involved  in  making  such 
a  table.  First,  the  numbers  from  i  to  74  are  divided  by  74,  giv¬ 
ing  the  percent  of  subjects  making  each  score.  Second,  since 
Rugg’s  table  provides  for  the  percent  failing,  it  is  necessary  to 
subtract  each  of  these  percents  from  100,  getting  the  percent 
below  each  score.  Third,  the  percentile3  corresponding  to  each 
number  obtained  in  the  second  step  is  taken  from  the  table.  An 
illustration  will  serve  to  make  the  method  clearer.  We  shall  take 
the  subject  making  the  highest  score.  He  ranks  number  1.  This 
number  divided  by  74  gives  1.35  percent.  If  we  subtract  1.35 
from  100,  we  get  98.65,  the  percent  of  subjects  below  the  best  one. 
The  percentile  in  the  table  corresponding  to  98.65  is  86.  Then 
86  is  the  percentile  rank  of  the  subject  having  the  highest  rank 
in  any  test  or  factor  of  a  test.  The  corresponding  percentiles  are 
found  in  this  manner  for  each  rank  and  then  it  is  necessary  only 
to  rank  the  subjects  by  the  usual  method  and  read  off  the  per¬ 
centiles  from  the  table. 

There  may  be  a  slight  objection  to  this  method  of  assigning 
percentiles.  The  question  may  well  be  asked  as  to  why  the 
scores  run  down  to  o  and  yet  up  only  to  86.  Why  should  they 
not  go  up  to  100?  By  this  method  the  upper  score  will  approach 
100  as  the  number  of  cases  is  increased.  If  we  think  of  the 
scale  as  a  continuous  one,  we  may  regard  o  as  extending  from 
o  to  14  and  86  as  extending  from  86  to  100.  It  would  probably 
have  been  a  little  more  correct  to  have  moved  each  score  up  a 
half  step  or  to  have  designated  its  middle  position  in  a  continuous 

2  Rugg,  H.  O.,  Statistical  Method  Applied  to  Education,  1917,  396  ff. 

3  Scores  are  assumed  to  fit  the  probability  curve  and  percentages  of  sub¬ 
jects  who  make  various  scores  correspond  to  percentages  of  area  under 
the  curve  from  the  o  point  to  a  point  on  the  base  line.  This  point  on  base 
line  is  measured  in  units  of  <r  and  is  transformed  into  percentile  scores  by  set¬ 
ting  o  at  — 3.0  (j,  50  at  the  mean  and  100  at  3.0 

Example:  A  subject  having  20  per  cent  of  the  subjects  below  him  will 
always  have  a  percentile  score  of  36. 


INTERRELATION  OF  HIGHER  LEARNING  PROCESSES 


3 


scale.  This  would  have  put  the  lowest  scale  at  7  and  the  high¬ 
est  at  93.  Certainly  there  would  have  been  no  difference  in  the 
results  as  far  as  correlations  are  concerned.  It  would  have 
thrown  the  mean  in  each  distribution  just  a  small  fraction  of  a 
unit  higher  and  would  not  have  changed  the  standard  deviations. 

The  reason  for  not  using  the  raw  scores  probably  needs  no 
defense  here.  The  percentiles  as  used  here  tend  to  give  a  more 
nearly  normal  distribution  than  that  given  by  the  raw  scores. 
Nearly  all  devices  for  handling  and  refining  data  are  based  on 
normal  distribution.  Probably  scores  that  give  a  normal  dis¬ 
tribution  are  more  nearly  correct  than  raw  scores.  Who  knows 
whether  five  minutes  consumed  at  the  beginning  of  the  experi¬ 
ment  is  just  as  significant  as  five  minutes  after  the  subject  has 
been  working  thirty  minutes?  Again,  is  there  any  evidence 
that  two  hundred  errors  mean  just  half  as  much  efficiency  as  one 
hundred?  Very  often  one  little  confusion  or  distraction  will 
cause  the  number  of  errors  to  be  doubled.  A  second  reason 
may  be  given  for  using  the  percentiles.  All  standard  deviation 
units  are,  for  all  practical  purposes,  equal4  and  thus  simplify 
analysis  by  the  use  of  regression  lines.  The  regression  of  x  on 
y  will  always  be  equal  to  y  on  x  when  the  standard  deviations  of 
the  two  arrays  are  equal.  Also  in  the  distribution  tables  the 
number  of  rows  will  be  equal  to  the  number  of  columns  and 
thus  make  the  regression  lines  less  likely  to  be  misinterpreted. 

After  the  data  have  all  been  reduced  to  percentiles,  the  next 
problem  is  to  determine  the  method  of  scoring  or  combining 
the  different  factors  in  the  test.  This  method  of  scoring  is  sec¬ 
ondary  to  that  of  analysis.  Such  questions  as  the  following 
must  be  answered:  Is  it  necessary  to  use  all  the  factors  in  the 
tests?  If  not,  what  ones  should  be  used?  The  answers  to  such 
questions  are  important  from  both  the  standpoint  of  scoring 
and  from  that  of  analysis.  The  answer  will  be  sought  by  using 
the  scores  in  the  Binet-Simon  Tests5  as  a  criterion  and  then  using 
partial  correlations. 

4  The  lowest  standard  deviation  is  15.56  and  the  highest  16.68.  The  exact 
standard  deviation  for  each  factor  and  test  will  be  given  later. 

5  Whenever  the  expression,  “Binet-Simon  Tests”  is  used,  the  Stanford 
Revision  is  meant. 


4 


B.  F.  H AUGHT 


Some  objections  could  be  raised  to  this  method  of  procedure. 
The  first  one  is  the  criterion  itself.  Does  it  include  all  factors 
in  tests  that  have  value?  Does  it  include  these  in  such  a  pro¬ 
portion  that  the  scores  are  the  best  ones?  No  attempt  will  be 
made  to  answer  these  questions  at  this  stage.  From  the  point 
of  view  of  this  study,  these  are  not  such  important  questions, 
since  the  criterion  as  well  as  the  experiments  will  be  analyzed. 
In  other  words  these  are  questions  that  should  be  answered 
after  the  experiments  have  been  analyzed.  The  scores  resulting 
from  the  combination  of  factors  will  have  no  value  other  than 
for  analysis  as  far  as  this  investigation  is  concerned.  The  tests 
have  some  other  serious  defects.  Only  those  will  be  mentioned 
that  apply  to  adults,  since  this  investigation  is  limited  entirely 
to  this  field.  It  is  claimed  that  the  Binet-Simon  tests  fail  to  dis¬ 
tribute  individuals  in  the  upper  quartile  widely  enough.  In  other 
words,  the  tests  are  too  easy  for  very  bright  adults.  The  highest 
intelligence  quotient  possible  is  122.  Some  of  the  individuals 
were  not  measured  accurately.  This  is  a  serious  objection  to  the 
tests  themselves.  For  this  study,  however,  it  is  not  so  serious  as 
it  would  be  where  the  object  was  to  determine  the  actual  in¬ 
telligence  quotients.  It  is  true  that  the  intelligence  quotients 
have  been  used,  but  only  the  ranking  of  them  was  used  in  deter¬ 
mining  the  percentiles.  It  is  reasonable  to  expect  that  the  rank¬ 
ing  of  the  subjects  by  intelligence  quotients  is  much  more  nearly 
correct  than  the  absolute  intelligence  quotients  themselves.  An¬ 
other  objection  is  that  the  tests  are  not  standardized  for  the 
upper  years.  This  objection  does  not  interfere  in  the  present 
cases,  since  it  is  only  the  ranking  of  the  subjects  in  intelligence 
quotients  that  is  used,  and  since  only  one  of  the  subjects  made 
the  highest  score  possible. 

Other  criteria  could  have  been  used.  The  school  grades 
in  the  various  subjects  could  have  been  combined  and  used.  This 
was  done  by  Rosenow.6  That  scheme,  however,  would  not  have 
worked  very  well  in  this  case,  since  the  subjects  had  different 
teachers  during  the  year  and  there  was  no  standard  to  unify  the 

6  Rosenow,  Curt,  The  Analysis  of  Mental  Functions,  Psychol.  Monog., 
1917,  24  (No.  106). 


INTERRELATION  OF  HIGHER  LEARNING  PROCESSES 


5 


grading.  There  are  other  reasons  why  academic  marks  are  not 
gfood  for  a  criterion.  Too  many  other  factors,  such  as  health, 
outside  attractions,  interest  in  the  subject,  etc.,  which  are  very 
often  not  known  by  the  teacher,  enter  into  the  grades  of  the 
students.  The  school  grade  is  certainly  not  as  significant  as  the 
Binet-Simon  tests  in  determining  intelligence.  This  fact  has 
already  been  pointed  out  by  psychologists.7  Another  criterion 
that  is  regarded  as  sound  by  some  is  the  combined  judgment  of 
instructors.8  This,  however,  has  its  limitations,  especially  for 
the  present  study,  where  no  instructors  could  be  selected  who 
were  acquainted  with  all  the  subjects.  This,  as  has  been  shown 
by  Thorndike,9  is  not  an  unsurmountable  difficulty.  Taking 
everything  into  consideration,  however,  there  probably  is  no  one 
thing  that  would  make  a  better  criterion  than  the  Binet-Simon 
tests.  This  criterion  could  have  been  made  much  better  if  it  had 
been  supplemented  with  other  tests  and  the  combined  results 
used.  The  Otis  tests  could  have  been  given  and  the  intelligence 
quotients  combined  with  those  in  our  criterion.  This,  however, 
was  not  thought  of  until  it  was  too  late  to  get  the  tests  and  ad¬ 
minister  them. 

The  second  objection  to  this  procedure  is  that  it  assumes 
linearity.  It  is  claimed  by  some  that  correlations  are  meaning¬ 
less  when  non-linearity  exists.  Rosenow10  has  given  the  best 
rebuttal  to  this  argument  that  has  come  to  the  writer’s  notice. 
He  says:  “It  follows  that,  taken  merely  as  an  indication  that 
an  actual  relation  does  exist  between  two  variables,  r,  the  co¬ 
efficient  of  correlation,  is  actually  entitled  to  increased  confidence 
if  non-linear  regression  is  shown.  Indeed  the  mere  proof  of 
non-linear  regression  is  in  and  of  itself  proof  of  the  existence 
of  a  true  relation,  and  also  of  the  fact  that  it  is  greater  than  in- 

7  E.  g.,  Peterson,  Joseph,  The  Rational  Learning  Test  Applied  to  Eighty- 
one  College  Students,  J.  of  Educ.  Psychol.,  1920,  11,  1 37  ff. 

8  Ruml,  Beardsley,  The  Reliability  of  Mental  Tests  in  the  Division  of  An 
Academic  Group,  Psychol.  Monog.,  1917,  24  (No.  105). 

9  Thorndike,  E.  L.,  Combining  Incomplete  Judgments  of  Relative  Position, 
I.  Phil.  Psychol,  and  Sc.  Methods,  1916,  13,  197  ff. 

10  Rosenow,  Curt,  The  Analysis  of  Mental  Functions,  Psychol.  Monog., 
1917,  24,  (No.  106),  10  f. 


6 


B.  F.  H AUGHT 


dicated  by  r.  It  can  hardly  be  claimed  that  a  positive  assertion 
which  errs  only  on  the  conservative  is  meaningless.  As  a  special 
case  we  may  note  that  r— o  does  not  necessarily  indicate  the  ab¬ 
sence  of  relation.”  Again  he  says:  “The  subject  of  non-linear 
regression  for  the  psychologist  amounts  simply  to  this.  If  he  is 
investigating  the  relation  of  two  variables  to  each  other  he  can 
get  nearest  the  truth  by  ‘fitting’  a  curve  and  determining  its 
equation.  Even  in  that  case  useful  results  are  practically  always 
obtainable  by  assuming  linearity.  But  if  one  is  dealing  with  a 
complex  situation  the  only  practical  possibility  with  our  present 
technique  is  to  assume  linearity.  The  results,  when  properly 
interpreted,  will  not  be  meaningless.” 

In  this  investigation  linearity  will  be  assumed  for  the  purpose 
of  calculating  correlations  and  combining  factors,  but  interpreta¬ 
tions  will  be  made  in  such  a  way  as  to  make  allowance  for  all 
cases  of  non-linearity.  That  is,  the  degree  of  non-linearity,  as 
shown  by  an  inspection  of  the  curves  through  the  means  of  the 
rows  and  columns,  will  be  noted  in  each  case. 

After  the  factors  in  the  tests  have  been  analyzed  in  the  light 
of  the  criterion,  the  investigation  will  be  carried  further  by  the 
use  of  multiple  correlation.  This  may  be  done  directly  from 
the  equation,11 


(r — ril)  (* 


r2 

13.2 


)  (i- 


14.23 


)  (  1 - ^*15. 234  ) 


16.2345. 


(0 


in  which  R  is  the  symbol  for  the  correlation  between  the  criterion 
I  and  the  factors  2,  3,  4,  5,  and  6  combined  in  such  a  way  as  to 
give  the  highest  correlation  possible.  It  is  possible  by  the  use 
of  this  formula  to  determine  what  factors  are  necessary  to  get 
the  highest  correlation.  If  some  factors  are  shown  by  partial 
correlations  to  have  nothing  in  common  with  the  criterion  ex¬ 
cept  what  is  contained  in  other  factors  and  then  the  formula 
for  multiple  correlation  shows  that  the  correlation  with  the 
criterion  is  not  reduced  by  discarding  these  factors,  there  is  no 
reason  for  using  them. 

11  Yule,  G.  U.,  Introduction  to  The  Theory  of  Statistics,  248  ff. 


INTERRELATION  OF  HIGHER  LEARNING  PROCESSES 


7 


Now  that  it  has  been  decided  just  what  factors  should  be  used, 
the  next  step  is  to  determine  the  best  combination  of  them. 
Must  they  be  combined  in  equal  proportion  or  in  some  other 
ratio?  To  determine  this  question,  the  following  formula  will 
be  used: 

o  (r  r  — r  ) 

p  Ml  IM  Mm  ; 

C  = - —  (2) 

0  ( r  r  — r  ) 
ni  Im  Mm  IM' 


in  which  M  is  the  major  factor,  m  the  minor  factor,  I  the  criterion 
and  C  a  constant  which  determines  how  m  shall  be  weighted  in 
order  to  give  the  highest  correlation  with  I  when  combined  with 
M.  In  order  to  find  this  highest  correlation  after  C  has  been 
determined,  the  following  formula  will  be  used : 

+  CrT  am 


r  <rM 
IM 


Im 


^M+Cmj'^V aM2  -f-  2Cr  ^^aMam  +  C2am2  (3) 

in  which  the  letters  have  the  same  meaning  as  in  formula12  (2). 
If  more  than  two  factors  need  to  be  combined  in  any  test,  two 
will  be  combined  in  the  best  way  and  then  this  result  with  the 
third  factor.  In  this  way  any  number  of  factors  or  tests  may 
be  combined. 

The  method  of  scoring  will  then  consist  of  four  steps :  first, 
the  determination  of  the  significant  factors  by  multiple  and  partial 
correlation;  second,  the  finding  of  the  best  combination  of  the 
significant  factors;  third,  the  determination  of  the  best  correla¬ 
tion  when  this  combination  is  used;  fourth,  actually  combining 
the  factors  and  working  out  the  correlation  to  test  the  reliability 
of  the  mathematical  work. 

Each  factor  will  be  further  analyzed  by  stating  the  theoretical 
relation  to  the  criterion  and  the  actual  relation  in  terms  of  the 
curves  of  the  means  of  the  columns  and  of  the  rows.  The  tables 
of  partial  correlations  will  be  freely  used  in  determining  the 
relation  of  each  factor  to  the  criterion  and  to  the  other  factors. 
For  example,  an  attempt  will  be  made  to  find  the  relation  of 


12  For  the  development  of  these  formulae,  see  Thurstone,  L.  L.,  A  Scoring 
Method  for  Mental  Tests,  Psychol.  Bull.,  1919,  r<5,  235  ff. 


8 


B.  F.  H AUGHT 


the  time  factor  to  the  criterion  and  then  to  the  other  factors  of 
repetitions  and  errors.  Special  cases  that  fall  below  the  fortieth 
percentile  in  one  test  and  above  the  sixtieth  in  another  will  be 
analyzed  as  far  as  objective  data  will  permit. 

III.  Subjects 

Eighty  college  students  were  tested  in  securing  the  data  for 
this  investigation.  All  were  in  the  same  course,  conducted  by 
the  writer  in  the  winter  and  spring  terms  of  the  school  year 
1919-20.  The  testing  began  early  in  January  and  continued  until 
the  first  week  in  June.  The  course  was  conducted  in  three  sec¬ 
tions.  One  section  was  begun  the  first  week  in  January  and  fin¬ 
ished  on  the  twenty-fifth  of  March.  The  other  two  were  begun 
the  last  week  in  March  and  finished  on  the  ninth  of  June.  Six 
of  the  subjects  tested  are  not  included  in  the  final  list  of  seventy- 
four  because  of  having  failed  to  take  all  the  tests  or  because  of 
having  been  coached  in  one  of  the  tests.  A  record  of  the  sex  and 
college  class  is  given  in  Table  I  for  each  subject. 

In  many  respects  this  represents  a  selected  group.  There  is 
considerable  uniformity  in  age,  education,  and  social  status.  The 
majority  are  high  school  graduates,  and  those  who  are  not  have 
in  some  other  kind  of  school  completed  work  sufficient  for  college 
entrance.  There  are  three  or  four  in  the  group  who  have  very 
low  intelligence.  These  have  browsed  around  here  and  there, 
gaining  a  few  credits  at  each  place,  until  they  were  able  to  get 
freshman  standing  in  a  college,  but  are  not  able  to  do  real  college 
work.  No  attempt  was  made  to  select  subjects  for  the  investi¬ 
gation.  The  aim  was  to  use  all  who  entered  a  certain  class  in 
education.  This  was  followed  as  nearly  as  possible,  the  only 
exception  being  in  the  case  of  six  students,  of  whom  four  left 
school  before  all  the  tests  were  taken  and  two  showed  evidence 
of  having  been  coached  on  one  of  the  experiments. 

IV.  The  Binet-Simon  Tests  ( Stanford  Revision ) 

In  every  instance  the  subject  was  first  given  the  tests  for  the 
average  adult.  If  he  passed  on  all  of  them  he  was  then  given  the 
tests  for  the  superior  adult;  but  if  he  failed  on  one  or  more  of 


INTERRELATION  OF  HIGHER  LEARNING  PROCESSES 


Table  I.  Showing  Sex  and  College  Class  of  Each  Subject. 


IS 

Subject 

Sex 

1 

College  Class 

Subject 

Sex 

I  College  Class 

i 

f 

Freshman 

38 

f 

Freshman 

2 

f 

44 

39 

m 

44 

3 

m 

ii 

40 

f 

Sophomore 

4 

f 

ii 

4i 

f 

Senior 

5 

m 

Sophomore 

42 

f 

Sophomore 

5 

f 

Freshman 

43 

f 

Freshman 

7 

f 

ii 

44 

f 

44 

8 

m 

ii 

45 

m 

44 

9 

f 

ii 

46 

m 

Sophomore 

IO 

m 

ii 

47 

f 

Freshman 

ii 

f 

ii 

48 

f 

44 

12 

m 

ii 

49 

f 

Sophomore 

13 

f 

ii 

50 

f 

Freshman 

14 

m 

ii 

5i 

m 

44 

15 

f 

ii 

52 

f 

ii 

16 

f 

ii 

53 

f 

ii 

17 

m 

(4 

54 

f 

a 

18 

f 

44 

55 

f 

a 

19 

f 

Senior 

56 

m 

a 

20 

f 

Freshman 

57 

f 

a 

21 

f 

44 

58 

f 

44 

22 

f 

Sophomore 

59 

f 

Sophomore 

23 

f 

Freshman 

60 

f 

Freshman 

24 

f 

44 

61 

f 

<4 

25 

f 

44 

62 

f 

44 

26 

f 

44 

63 

f 

44 

27 

f 

44 

64 

f 

44 

28 

f 

Sophomore 

65 

f 

44 

29 

f 

Junior 

66 

m 

Freshman 

30 

f 

Freshman 

67' 

f 

Sophomore 

31 

f 

Sophomore 

68 

m 

44 

32 

f 

44 

69 

f 

44 

33 

m 

Freshman 

70 

f 

Freshman 

34 

m 

44 

7i 

f 

44 

35 

f 

Sophomore 

72 

f 

44 

36 

f 

Freshman 

73 

f 

44 

37 

f 

44 

74 

f 

44 

Table  II.  Showing  Summary  of  Subjects. 


1 

Freshman 

Sophomore 

Junior 

Senior 

Totals 

Male 

13 

3 

0 

0 

16 

Female 

44 

11 

1 

2 

58 

Totals 

57 

14 

1 

2 

74 

13  The  numbers  assigned  to  the  several  subjects  in  this  table  will  be  used 
in  all  following  tables. 


10 


B.  F.  H AUGHT 


them  he  was  then  given  the  tests  for  fourteen  years  of  age.  In 
case  all  the  tests  in  this  year  were  not  passed,  the  twelve  year 
tests  were  given.  In  no  case  was  it  necessary  to  go  further  back 
and  in  very  few  back  so  far.  If  the  subject  did  one  or  more  of 
the  tests  for  the  average  adult  correctly,  he  was  given  the  tests 
for  the  superior  adult  also.  The  mental  age  and  the  intelligence 
quotient  were  found  for  each  subject  in  the  manner  suggested  by 
Terman.14  Table  III  gives  the  intelligence  quotient  and  the  per¬ 
centile  rank  for  each  subject. 

Table  III.  Showing  Intelligence  Quotient  and  Percentile  Rank  for 
Each  Subject  in  the  Binet-Simon  Tests. 


Subject 

Intelligence 

Quotient 

Percentile 

Rank 

Subject 

Intelligence 

Quotient 

Percentile 

Rank 

1 

11 3 

69 

38 

82 

21 

2 

116 

78 

39 

no 

63 

3 

98 

42 

40 

9 6 

39 

4 

106 

54 

41 

107 

58 

5 

122 

86 

42 

109 

60 

6 

91 

30 

43 

94 

35 

7 

104 

52 

44 

95 

37 

8 

76 

0 

45 

99 

45 

9 

80 

18 

46 

no 

63 

10 

9i 

30 

47 

102 

49 

11 

1 13 

69 

48 

101 

47 

12 

99 

45 

49 

no 

63 

13 

95 

37 

50 

103 

5i 

14 

96 

39 

5i 

98 

42 

15 

106 

54 

52 

107 

58 

16 

106 

54 

53 

93 

34 

1 7 

83 

23 

54 

101 

47 

18 

105 

53 

55 

101 

47 

19 

H3 

69 

56 

98 

42 

20 

96 

39 

57 

104 

52 

21 

92 

32 

58 

no 

63 

22 

95 

-  37 

59 

101 

47 

23 

98 

4 2 

60 

78 

14 

24 

116 

78 

61 

116 

78 

2  5 

98 

42 

62 

1 13 

69 

26 

no 

63 

63 

113 

69 

2  7 

99 

45 

64 

103 

5i 

28 

101 

47 

1  65 

107 

58 

29 

104 

52 

|  66 

113 

69 

30 

102 

49 

6  7 

107 

58 

3i 

107 

58 

68 

113 

69 

32 

93 

34 

69 

107 

58 

33 

87 

27 

70 

116 

78 

34 

113 

69 

7i 

85 

25 

35 

99 

45 

72 

no 

63 

36 

93 

34 

73 

104 

52 

37 

109 

60 

74 

9i 

30 

14  Terman,  The  Measurement  of  Intelligence,  1916. 


INTERRELATION  OF  HIGHER  LEARNING  PROCESSES 


ii 


V.  The  Rational  Learning  Test 

(i)  Description  of  Test  and  Method  of  Scoring. 

In  this  test  the  procedure  of  the  author15  was  followed  as  nearly 
as  possible.  The  instructions  to  the  subject  and  the  method  of 
recording  the  data  were  identical.  Some  variations  occur  in 
the  scoring,  as  will  appear  later.  The  instructions  to  the  subject 
follow : 

“This  is  a  memory-reason  test.  The  letters  A,  B,  C,  D,  E,  F, 
G,  H,  I  and  J  are  numbered  in  a  random  order  from  i  to  io.  I 
call  out  the  letters  in  their  order  and  you  are  to  guess  for  each 
letter  till  you  get  the  correct  number,  when  I  say  'Right.’  Then 
I  call  out  the  next  letter,  and  so  on.  This  is  continued  until  you 
get  each  number  right  the  first  guess  twice  in  succession  through 
the  series,  from  A  to  J.  Then  you  are  through.  You  must  ask 
no  questions,  but  are  to  use  all  the  mental  powers  at  your  com¬ 
mand.  You  will  be  judged  by  ( i )  the  total  time  you  take,  (2)  the 
number  of  errors  or  wrong  guesses  you  make  (every  number  you 
speak  being  a  guess),  and  (3)  the  number  of  repetitions  from 
A  to  J  that  you  require  for  the  learning.  Re-read  these  instruc¬ 
tions  carefully,  if  necessary,  to  understand  what  you  are  to  do. 
The  meaning  will  be  clearer  as  we  go  on  with  the  experiment.” 

The  subject  was  seated  at  a  table  opposite  the  experimenter 
and  shielded  from  the  latter  by  a  screen.  He  was  given  a  type¬ 
written  copy  of  the  instructions  and  allowed  to  read  and  study 
them  until  he  was  ready  to  go  on  with  the  learning.  He  usually 
consumed  about  one  minute.  When  the  subject  said  he  was  ready 
to  proceed,  a  stop  watch  was  started,  the  letters  called  out  in  their 
order,  and  the  responses  recorded  as  shown  in  Table  IV.  When 
the  learning  was  complete,  the  total  time  was  recorded  and  the 
subject  asked  to  write  as  much  as  he  could  about  how  he  learned 
to  repeat  the  numbers  in  order. 

15  Peterson,  Joseph,  Experiments  in  Rational  Learning,  Psychol.  Rev.,  1918, 
25,  433  ff . 


12 


B.  F.  H AUGHT 


Table  IV.  Showing  Record  of  Subject  Number  68  and 
Method  of  Recording  Data. 


Letters 

1 

A 

B 

€ 

D 

E  1 

F 

G 

H| 

i 

i 

J 

Errors 

Numbers 

6 

4 

9 

i 

8 

IO 

3 

1 

2 

7 

5 

Uc. 

t 

♦ 

Total 

First 

6 

3 

i 

10 

2 

2 

2 

2 

9t 

5 

Repetition 

5 

3 

8 

3 

3 

3 

7 

9 

2 

7 

5 

5 

8 

5 

5 

7 

7 

7 

6+ 

3 

8 

8f 

4 

7 

2 

IO 

8 

I 

9 

29 

3 

0 

32 

Second 

6 

4 

9 

2 

8 

3 

3 

8+ 

3t 

3t 

Repetition 

I 

4t 

7 

5 

5 

5 

3t 

7 

2 

2 

7 

8+ 

9t 

5* 

IO 

15 

7 

I 

23 

Third 

6 

4 

9 

I 

10 

9t 

7 

7 

7 

5 

Repetition 

8 

2 

8t 

9t 

3 

2 

2 

7 

It 

8f 

3 

*9f 

IO 

13 

6 

I 

20 

Fourth 

6 

4 

9 

I 

IO 

2 

3 

2 

7 

5 

Repetition 

8 

7 

8f 

9+ 

IO 

5 

2 

0 

7 

Fifth 

6 

4 

8 

I 

10 

2 

3 

2 

7 

5 

Repetition 

9 

8 

2 

o 

o 

i 

Sixth 

6 

4 

9 

I 

10 

IO 

3 

2 

7 

5 

Repetition 

8 

I 

o 

0 

i 

Seventh 

Repetition 

6 

4 

9 

I 

8 

IO 

3 

2 

7 

5 

0 

0 

0 

0 

Eighth 

Repetition 

6 

4 

l  9 

I 

8 

IO 

3 

2 

7 

5 

O 

0 

o 

o 

Totals 

1 

I 

65 

18 

2 

1  85 

INTERRELATION  OF  HIGHER  LEARNING  PROCESSES 


1 3 


Three  schedules  of  numbers  were  used  in  giving  this  test. 
Subjects  12,  15,  20,  21,  22,  25,  31,  34,  35,  37,  39,  40,  44,  47, 

49 >  52>  53>  54>  57>  59>  62,  66,  67,  68,  69,  and  74  used  schedule  i.16 
Subjects  1,  2,  5,  6,  7,  8,  10,  13,  14,  17,  18,  19,  28,  29,  30,  36, 
38>  5°>  55>  56,  60,  63,  70,  72,  and  73  used  schedule  2. 17  Sub¬ 
jects  3,  4,  9,  11,  16,  23,  24,  26,  27,  32,  33,  41,  42,  43,  45,  46, 
48,  51,  58,  61,  64,  65  and  71  used  schedule  3. 18 

The  numbers  were  arranged  according  to  no  special  method. 
Schedule  2  is  that  used  by  Dr.  Peterson19  in  some  of  his  work. 
Schedules  1  and  3  were  made  with  the  idea  of  having  them  equal 
in  difficulty  to  2.  This,  of  course,  makes  the  statement  as  to 
random  numbering  in  the  directions  to  the  subject  slightly  in¬ 
correct,  but  each  schedule  could  be  obtained  by  a  random  selection. 
Therefore  the  statement  should  put  the  subject  to  no  disadvan¬ 
tage.  From  observation  there  is  no  difference  in  the  difficulty  of 
the  schedules.  The  orders  3-2,  5-4,  and  6-5  in  schedules  1,  2,  and 
3  respectively  present  especial  difficulty  to  many  subjects.  The 
purpose  in  having  different  schedules  was  to  reduce  probability 
of  coaching.  There  was  no  evidence  of  coaching  in  this  test. 
Each  subject  was  asked  after  the  test  was  performed  not  to  tell 
any  other  member  of  the  class  anything  that  might  assist  in  the 
learning. 

The  column  headed  Uc.  in  this  table  gives  the  unclassified  er¬ 
rors,  or  the  total  number  of  errors  regardless  of  kind. 

Errors  marked  f  are  called  logical  errors.  They  are  errors 
which  consist  in  guessing  a  number  that  has  already  been  used 
for  an  earlier  letter  of  the  series,  one  that  could,  therefore,  not 
possibly  be  right. 

Errors  marked  *  are  called  perseverative  errors.  They  are 
errors  which  consist  in  repeating  a  wrong  guess  while  reacting 


to  a  single  letter. 

16  Schedule  1 

A 

B 

C 

D 

E 

F 

G 

H 

I 

J 

6 

4 

9 

I 

8 

10 

3 

2 

7 

5 

17  Schedule  2 

A 

B 

C 

D 

E 

F 

G 

H 

I 

J 

9 

6 

2 

10 

8 

1 

5 

4 

7 

3 

18  Schedule  3 

A 

B 

C 

D 

E 

F 

G 

H 

I 

J 

4 

8 

3 

1 

9 

7 

10 

6 

5 

2 

19  Peterson,  Joseph,  Experiments  in  Rational  Learning,  Psychol.  Rev.,  1918, 
25,  433  ff- 


14 


B.  F.  H AUGHT 


In  Table  V  are  given  the  raw  scores  of  all  the  subjects,  and 
also,  on  the  right  hand  side  of  the  table,  the  scores  converted 
into  percentile  rank  and  the  final  combined  score.  This  combined 
score  for  the  test  is  determined  by  combining  the  percentile  rank 
in  repetitions  and  in  perseverative  errors  and  then  converting 
into  percentile  score  from  Rugg’s  table,  as  will  presently  be  ex¬ 
plained.  Tables  VI  and  VII  show,  respectively,  the  total  and  the 
partial  correlations  of  each  factor  in  the  Rational  Learning  Test 
with  the  criterion,  the  Binet-Simon  tests,  and  the  total  and  the 
partial  correlations  of  the  factors  in  the  Rational  Learning  Test. 

Table  V.  Showing  the  Number  of  Minutest,  the  Number  of  Repetitions, 
the  Number  of  Each  Kind  of  Errors,  and  the  Percentile  Rank  for 
Each  Kind  of  Data  in  Rational  Learning. 


Subject 

Raw  Score  in 

Percentile  Rank  in 

|  Time 

|  Rep. 

Uc.E. 

L.E. 

P.E. 

Time 

Rep. 

Uc.E. 

1 

L.E. 

1 

P.E. 

1 

ScoreJ 

I 

3 

4 

27 

0 

0 

86 

76 

72 

82 

71 

78 

2 

1 7 

8 

124 

64 

3 

42 

46 

35 

30 

55 

52 

3 

14 

7 

96 

34 

13 

46 

53 

42 

45 

35 

40 

4 

18 

8 

71 

8 

3 

40 

46 

5o 

63 

55 

52 

5 

5 

4 

56 

23 

0 

74 

76 

57 

49 

7i 

78 

6 

6 

3 

23 

0 

0 

72 

85 

76 

82 

7i 

84 

7 

17 

11 

64 

13 

1 

42 

35 

53 

57 

63 

49 

8 

21 

14 

196 

78 

38 

3i 

25 

21 

21 

23 

18 

9 

12 

7 

21 

2 

0 

53 

53 

79 

73 

7i 

65 

IO 

19 

11 

113 

34 

15 

36 

35 

37 

45 

28 

28 

ii 

18 

9 

47 

10 

3 

40 

42 

61 

59 

55 

48 

12 

20 

14 

240 

143 

12 

33 

25 

18 

18 

38 

28 

13 

7 

5 

59 

13 

4 

69 

68 

55 

57 

5i 

61 

14 

20 

11 

168 

66 

3 

33 

35 

28 

28 

65 

44 

15 

16 

6 

53 

28 

3 

44 

61 

59 

47 

55 

59 

16 

7 

4 

44 

6 

4 

69 

76 

65 

66 

5i 

68 

17 

25 

15 

169 

72 

11 

25 

16 

27 

23 

40 

22 

18 

14 

9 

81 

28 

5 

46 

42 

46 

47 

48 

44 

19 

9 

7 

93 

38 

7 

61 

53 

43 

42 

45 

49 

20 

13 

10 

62 

18 

5 

49 

38 

54 

53 

48 

38 

21 

12 

9 

79 

42 

3 

53 

42 

46 

38 

55 

48 

22 

8 

6 

105 

44 

6 

65 

61 

40 

35 

46 

56 

23 

18 

12 

130 

58 

0 

40 

31 

3i 

32 

7i 

53 

24 

8 

8 

43 

9 

2 

65 

46 

65 

61 

59 

56 

25 

17 

14 

109 

31 

3 

42 

25 

39 

46 

55 

36 

26 

16 

10 

88 

34 

17 

24 

38 

45 

45 

25 

28 

27 

12 

7 

88 

35 

4 

53 

53 

45 

43 

5i 

54 

28 

12 

7 

53 

16 

0 

53 

53 

59 

54 

7i 

65 

29 

14 

7 

75 

21 

6 

46 

53 

48 

50 

46 

51 

30 

10 

6 

35 

1 

4 

59 

61 

69 

76 

5i 

58 

31 

33 

14 

no 

36 

13 

0 

25 

38 

43 

35 

25 

32 

12 

7 

72 

40 

2 

53 

53 

49 

40 

59 

59 

INTERRELATION  OF  HIGHER  LEARNING  PROCESSES 


i5 


Table  V  (Continued) 


Subject 

.1 

Raw  Score  in 

Percentile  Rank  in  | 

Time 

1 

Rep. 

Uc.E. 

L.E. 

P.E. 

Time 

Rep. 

Uc.E. 

L.E. 

P.E. 

Scoret 

1 

33 

18 

12 

1 16 

38 

II 

40 

31 

36 

42 

40 

34 

34 

13 

13 

129 

41 

2 

49 

28 

32 

38 

59 

40 

35 

10 

5 

45 

5 

2 

59 

68 

63 

68 

58 

68 

36 

19 

7 

87 

36 

13 

36 

53 

45 

43 

35 

40 

37 

8 

8 

47 

9 

O 

65 

46 

61 

61 

7i 

60 

38 

30 

11 

178 

7 1 

13 

18 

35 

23 

25 

35 

33 

39 

5 

3 

23 

4 

0 

74 

85 

76 

7 1 

7 1 

84 

40 

11 

6 

75 

23 

10 

57 

61 

48 

49 

40 

52 

4i 

9 

5 

4i 

7 

0 

61 

68 

67 

65 

7 1 

73 

42 

20 

12 

174 

54 

13 

33 

3i 

25 

33 

35 

32 

43 

11 

6 

38 

10 

I 

57 

61 

68 

59 

63 

65 

44 

17 

8 

106 

20 

10 

42 

46 

40 

5i 

40 

38 

45 

19 

6 

65 

19 

12 

36 

61 

52 

52 

38 

51 

46 

13 

5 

48 

13 

3 

49 

68 

60 

57 

55 

62 

47 

22 

9 

126 

47 

28 

29 

42 

33 

35 

23 

3i 

48 

12 

9 

62 

7 

5 

53 

42 

54 

65 

48 

44 

49 

9 

5 

44 

14 

2 

61 

68 

65 

56 

59 

68 

50 

19 

10 

146 

43 

35 

36 

38 

30 

36 

18 

22 

5i 

24 

9 

hi 

42 

14 

27 

42 

38 

38 

3i 

35 

52 

12 

7 

55 

10 

4 

53 

53 

58 

59 

5i 

54 

53 

11 

9 

90 

40 

8 

57 

42 

43 

40 

44 

38 

54 

13 

8 

56 

12 

5 

49 

46 

57 

58 

48 

45 

55 

19 

9 

98 

59 

5 

36 

42 

4i 

3i 

48 

44 

56 

32 

15 

463 

267 

73 

14 

16 

0 

0 

0 

0 

57 

26 

21 

398 

206 

28 

23 

0 

14 

14 

23 

14 

58 

10 

7 

59 

18 

9 

59 

53 

55 

53 

42 

46 

59 

15 

8 

97 

48 

9 

45 

46 

42 

34 

42 

40 

60 

7 

8 

24 

5 

0 

69 

46 

73 

68 

7 1 

60 

61 

14 

5 

72 

23 

9 

46 

68 

49 

49 

42 

57 

62 

8 

6 

45 

7 

1 

65 

61 

63 

65 

63 

65 

63 

4 

6 

29 

5 

0 

82 

61 

70 

68 

7 1 

70 

64 

8 

7 

4i 

4 

0 

65 

53 

67 

7i 

7 1 

65 

65 

5 

5 

1 7 

0 

0 

74 

68 

86 

82 

7 1 

73 

66 

11 

6 

69 

19 

2 

57 

61 

5i 

52 

59 

61 

67 

14 

11 

124 

68 

9 

46 

35 

35 

27 

42 

35 

68 

8 

8 

65 

18 

2 

65 

46 

52 

53 

59 

56 

69 

12 

7 

70 

14 

8 

53 

53 

5i 

56 

44 

48 

70 

5 

5 

20 

1 

0 

74 

68 

82 

76 

7 1 

73 

7i 

9 

5 

58 

10 

13 

61 

68 

56 

59 

35 

53 

72 

28 

6 

76 

20 

15 

21 

61 

47 

5i 

28 

42 

73 

22 

7 

1 16 

24 

14 

29 

53 

36 

48 

3i 

37 

74 

13 

7 

54 

8 

8 

49 

53 

58 

63 

44 

48 

t  The  time  is  given  to  the  nearest  minute. 

t  Scores  are  found  by  adding  the  percentile  rank  in  repetitions  to  the  per¬ 
centile  rank  in  perseverative  errors  and  then  again  reducing  to  absolute 
percentiles  by  Rugg’s  table.  The  reason  for  this  will  appear  later. 


i6 


B.  F.  H AUGHT 


Table  VI.  Showing  Correlations!  and  Partial  Correlations  of  Each  Factor! 
of  the  Rational  Learning  Test  with  the  Binet-Simon  Tests.  The 
symbol  for  correlation  has  been  omitted.  The  table  should  read 

ri2  =  -27’  ri2.3  =  •°8>  etC- 


12 

.27 

13 

.31 

14 

.25 

15 

.23 

16 

.27 

12-3 

.08 

132 

.14 

14-2 

.05 

15-2 

.04 

16-2 

.15 

124 

.14 

13-4 

•  17 

14-3 

.02 

15-3 

.02 

16-3 

.18 

12-5 

.16 

13-5 

.20 

14-5 

.11 

15-4 

—.02 

16-4 

•  17 

12-6 

.10 

13-6 

.18 

14-6 

•03 

156 

.05 

16-5 

.19 

12-34 

.09 

13-24 

.14 

14-23 

— .02 

15-23 

— .02 

16-23 

.16 

12-35 

.08 

1325 

.14 

14-25 

.04 

14-24 

— .01 

16-24 

.14 

12-36 

— .02 

13-26 

.15 

14-26 

—.03 

15-26 

.01 

16-25 

•  14 

12-45 

.14 

13-45 

.17 

14-35 

.00 

15-34 

.00 

16-34 

.22 

12-46 

.10 

13-46 

.22 

14-36 

—.14 

15-36 

—.07 

i6-35 

.18 

12-56 

.09 

13-56 

.19 

14-56 

— .02 

15-46 

.04 

i6-45 

•  17 

12-345 

.09 

13-245 

.14 

14235 

— .01 

15-234 

.00 

16-234 

.20 

12-346 

.01 

13-246 

.20 

14-236 

—.14 

15-236 

—.07 

16-235 

.16 

12-356 

.00 

13-256 

.16 

14-256 

—.03 

15-246 

.04 

16-245 

.14 

12-456 

.10 

I3-456 

.24 

I4-356 

—.15 

I5-346 

.08 

16-345 

.23 

12-3456 

.01 

13-2456 

.21 

142356 

—.14 

15-2346 

.08 

16-2345 

.21 

f  All  correlations  are  worked  by  the  product-moment  method. 

$  For  the  sake  of  brevity  the  factors  are  designated  by  numbers  as  follows : 

1.  Binet-Simon  Tests  4.  Unclassified  Errors 

2.  Time  5.  Logical  Errors 

3.  Repetitions  6.  Perseverative  Errors 


Table  VII.  Showing  Correlations  and  Partial  Correlations  of  the 
Factors  in  the  Rational  Learning  Test. 


23 

.72 

24 

.78 

25 

.72 

26 

.69 

34 

•78 

23-4 

.28 

243 

•50 

25-3 

•43 

26-3 

•55 

34-2 

•50 

235 

•43 

24-5 

.46 

25-4 

—.07 

26-4 

.26 

34-5 

.48 

23-6 

.60 

24-6 

•55 

25-6 

.26 

26-5 

•43 

34-6 

.72 

23-45 

.27 

24-35 

.30 

25-34 

—.04 

26-34 

•34 

34-25 

•34 

23-46 

•37 

24-36 

.22 

25-36 

.24 

26-35 

•44 

34-26 

•57 

23-56 

•44 

24-56 

.28 

25-46 

.00 

26-45 

.23 

34-56 

•55 

23  456 

•37 

24-356 

•03 

25-346 

.10 

26-345 

•34 

34-256 

•50 

35 

•71 

36 

•49 

45 

•94 

46 

•75 

56 

.64 

35-2 

•40 

36-2 

.00 

45-2 

.87 

46-2 

•47 

56-2 

•29 

35-4 

— .12 

36-4 

—.23 

45-3 

.88 

46-3 

.67 

56-3 

•45 

35-6 

•59 

36-5 

.07 

45-6 

.91 

46-5 

•59 

56-4 

—•30 

35-24 

— .10 

36-24 

—•32 

45-23 

.84 

46-23 

•55 

56-23 

•30 

35-26 

.41 

36-25 

—.14 

45-26 

.88 

46-25 

•47 

56-24 

—.28 

35-46 

—.24 

36-45 

—.30 

45-36 

.87 

46-35 

.64 

56-34 

—•33 

35-246 

— .22 

36-245 

—.36 

45-236 

.85 

46-235 

•58 

56-234 

—•34 

If  we  consider  the  size  of  the  probable  error,20  it  seems  safe 
to  infer  from  the  data  in  Table  VI  that  repetitions  and  persever- 


20  The  probable  error  for  74  cases  is  .075  for  zero  correlation  and  .063  for 
a  correlation  of  .40.  The  probable  errors  are  not  given  in  each  instance,  since 
they  are  available  in  tables. 


INTERRELATION  OF  HIGHER  LEARNING  PROCESSES  17 


ative  errors  have  elements  in  common  with  the  criterion  that  are 
not  common  to  the  other  factors  or  to  each  other.  This  con¬ 
clusion  is  based  on  the  correlations,  r13.2456  and  r16.2345,  which  are 
.21  in  each  case.  This  is  three  times  the  probable  error  and  may 
be  regarded  as  significant.  Then  if  it  is  desired  to  score  the 
Rational  Learning  Test  so  as  to  have  it  correlate  highest  with 
the  Binet-Simon  tests,  these  two  factors  must  be  included.  It 
is  evident  that  time,  unclassified  errors,  and  logical  errors,  have 
nothing  in  common  with  the  criterion  that  is  not  included  in  the 
other  four  factors,  if  we  hold  that  a  correlation  less  than  three 
times  the  probable  error  is  not  significant.  It  must  also  be  kept 
in  mind  in  this  case  that  linearity  is  assumed.  To  be  more  specific, 
the  expression,  r12.3456=.oi,  means  that  everything  common  to 
1  and  2  is  contained  in  3,  4,  5  and  6.  Then  factor  2,  time,  may 
be  discarded  if  the  remaining  four  are  used.  Further,  since 
r15.346=.o8,  factor  5,  logical  errors,  may  be  discarded.  In  like 
manner,  since  r14.36=-.i4,  it  is  fairly  safe  to  discard  factor  4, 
unclassified  errors.  It  is  true  that  a  correlation  of  -.14  may  be 
slightly  significant.  It  may  mean  that,  if  the  elements  in  re¬ 
petitions  and  perseverative  errors  are  removed,  the  more  intelli¬ 
gent  the  subject  the  more  errors  he  will  make.  Let  the  question 
be  pushed  further  by  the  use  of  multiple  correlation.  By  the  use 
of  formula  (1),  it  is  found  that 

■^■1(23456)  *33 

But  R,(se)  =  -32 

The  difference  between  the  correlation  with  the  criterion  when 
all  five  factors  are  used  and  when  repetitions  and  perseverative 
errors  only  are  used  is  small  enough  to  be  entirely  neglected. 
This  is  further  evidence  that  factors  3  and  6  are  sufficient  to 
use  in  the  final  scores.  The  correlation  would  be  lowered,  if  any¬ 
thing  were  lost  by  discarding  the  others. 

The  next  step  is  to  find  the  proper  combination  of  these  two 
factors  to  give  the  best  correlation.  That  is,  must  they  be  com¬ 
bined  equally  or  in  some  other  proportion?  To  determine  this, 
formula  (2)  will  be  used.  Repetitions  will  be  designated  as  the 


i8 


B.  F.  H AUGHT 


major  factor  and  perseverative  errors  as  the  minor  factor.  The 
fundamental  constants  for  determining  C  are : 


rIM 

=  -3i 

rlm 

=  .27 

rMm 

=  49 

<7 

M 

=  16.35 

C J 

m 

=  I5-56 

When  these  values  are  substituted  in  formula  (2),  the  result  is 
1.05,  or  for  all  practical  purposes  1.  This  means  that  the  two 
combined  equally  will  give  the  best  correlation.  To  determine 
what  the  correlation  will  be  when  the  two  factors  are  combined 
equally,  formula  (3)  will  be  used,  in  which  the  letters  have  the 
same  meaning  as  in  formula  (2).  The  correlation  is  found  to 
be  .33.  The  actual  correlation  when  the  scores  in  repetitions  and 
perseverative  errors  are  combined  equally  is  .324. 

The  final  scores  are  found  by  adding  the  percentile  rank  in 
repetitions  to  the  percentile  rank  in  perseverative  errors  and  then 
again  using  Rugg’s  table  for  reducing  to  absolute  percentiles  as 
was  done  with  the  raw  scores. 

Multiple  correlation  indicated  that  a  correlation  of  .32  could 
be  obtained  by  combining  repetitions  and  perseverative  errors. 
Formula  (2)  indicated  that  the  best  combination  is  that  in  which 
they  are  combined  equally.  Formula  (3)  indicated  that  a  cor¬ 
relation  of  .33  should  be  obtained  when  they  are  combined  equally. 
When  the  actual  combination  is  made  and  the  correlation  is 
worked  out,  the  result  is  .324.  The  difference  between  these 
two  numbers  is  small  enough  to  be  accounted  for  by  the  way 
fractions  are  carried  out,  and  by  using  1  instead  of  1.05  as  a 
ratio  for  combining. 

(2)  Analysis  of  Data. 

There  is  a  “present  but  low”21  positive  correlation  in  this  test 

21  Correlations  below  .20  will  be  considered  negligible;  from  .20  to  .40, 
present  but  low ;  from  .40  to  .60,  marked ;  above  .60,  high.  See  Rugg,  H.  O., 
Statistical  Methods  Applied  to  Education,  1917,  256. 


INTERRELATION  OF  HIGHER  LEARNING  PROCESSES 


19 


between  the  criterion  and  each  of  the  factors.  In  other  words, 
there  is  slight  evidence  that  ability  in  the  criterion  and  ability  in 
each  factor  of  the  test  accompany  each  other.  Subjects  above 
the  average  in  the  former  will  be  above  the  average  in  each  of 
the  latter.  Since  the  variability22  is  made  the  same  in  each  kind 
of  data  by  reducing  to  absolute  percentiles,  a  change  in  one  test 
or  factor  will  be  accompanied  by  a  like  change  in  the  other 
test  or  factor,  and  equal  to  the  correlation  of  the  two  tests  or 
factors.  Thus,  time  and  the  criterion  have  a  correlation  of  .27. 
Therefore,  every  unit-change  in  one  will  be  accompanied  by  a 
like  change  of  .27  of  a  unit  in  the  other.  In  like  manner,  each 
of  the  other  factors  may  be  compared  with  the  criterion  by  refer¬ 
ence  to  the  correlations  in  Table  VI.  When  the  standard  devia¬ 
tions  are  equal,  the  regression  line  for  the  columns  takes  the  form 
y  =  rx  and  that  for  the  rows  takes  the  form  x  =  ry. 

Each  factor  in  this  test  has  something  common  to  the  criterion. 
Repetitions  have  most  and  unclassified  errors  least.  There  is, 
moreover,  a  great  overlapping  of  common  elements.  Thus  re¬ 
petitions  contain  all  that  is  common  to  time  and  the  criterion,  all 
that  is  common  to  unclassified  errors  and  the  criterion,  and  all 
that  is  common  to  logical  errors  and  the  criterion.  Time  has  all 
that  is  in  logical  or  unclassified  errors  with  respect  to  the  criterion. 
Unclassified  and  logical  errors  have  practically  the  same  elements 
as  far  as  the  criterion  is  concerned.  Repetitions  and  perseverative 
errors  have  something,  however,  not  found  in  any  one  of  the 
other  factors  or  in  any  combination  of  them.  These  two  contain 
everything  in  all  the  factors  needed  to  get  the  highest  correlation 
with  the  criterion. 

We  shall  use  Blakeman’s  criterion23  for  linearity.  When  the 
proper  values  substituted  in  the  formula  give  a  result  greater  than 
2.5,  non-linearity  will  be  said  to  exist  and  a  table  will  be  con¬ 
structed  showing  the  lines  of  the  means  of  the  rows  and  the 

22  The  standard  deviations  for  the  Binet-Simon  Tests,  time,  repetitions, 
unclassified  errors,  logical  errors  and  perseverative  errors  are  respectively 
16.62,  1647,  16.36,  16.68,  16.56,  and  15.56. 

23  For  formula,  see  Rugg,  Statistical  Methods  Applied  to  Education,  1917, 
283. 


20 


B.  F.  H AUGHT 


means  of  the  columns.  If  the  result  is  less  than  2.5,  the  correl¬ 
ation  is  for  all  practical  purposes  linear  and  no  table  of  regression 
lines  will  be  constructed. 

The  correlation-ratios  for  each  of  the  factors  with  the  criterion 
are  as  follows: 

12  =  .46  and  .52 

13  =  .41  and  .47 

14  =  .47  and  .52 

15  =  .44  and  .49 

16  =  .37  and  .40 

These  values  substituted  in  the  Blakeman  formula  give  results  as 
follows : 


Tests  1  and  2, 
Tests  1  and  3, 
Tests  1  and  4, 
Tests  1  and  5, 

Tests  1  and  6, 


2.37  and  2.83 
1. 71  and  2.25 
2.54  and  2.90 
2.39  and  2.  76 

1. 61  and  1.88 


According  to  Blakeman’s  criterion,  the  correlations  of  repetitions 
and  perseverative  errors  with  The  Binet-Simon  tests  are  linear, 
but  the  correlations  of  time,  unclassified,  and  logical  errors  with 
The  Binet-Simon  tests  are  non-linear.  The  regression  lines  for 
the  last  three  correlations  are  now  ready  to  be  constructed. 

The  regression  lines  showing  the  correspondence  between 
scores  in  time  and  the  criterion  are  shown  in  Table  VIII.  Each 
asterisk  indicates  the  position  of  one  person  as  determined  by 
both  tests.  The  circles  through  which  the  broken  line  passes 
represent  the  means24  of  the  columns  and  those  through  which 
the  whole  line  passes  represent  the  means  of  the  rows.  This  table 
shows  that  the  two  sets  of  relationships  are  in  very  close  agree¬ 
ment.  That  is,  the  regression  of  the  x-values  on  y  is  very  nearly  the 
same  as  the  y-values  on  x.  The  x-values  show  a  tendency  to  in¬ 
crease  constantly  with  an  increase  in  y-values  from  the  fortieth 
percentile  up.  Below  this  point  there  is  little  relation  between  x 
and  y-values.  The  y-values  have  a  tendency  to  increase  constantly 


24  The  means  for  the  columns  or  rows  are  found  by  adding  the  exact  per¬ 
centile  ranks  in  each  row1  or  column  and  dividing  by  the  number  of  cases. 


INTERRELATION  OF  HIGHER  LEARNING  PROCESSES 


21 


Table  VIII.  Showing  the  Distribution  of  Subjects  on  the  Basis  of  Time  in 
Rational  Learning  and  the  Binet-Simon  Tests.  Circles  through  which 
the  broken  line  passes  represent  the  means  of  the  columns  and  those 
through  which  the  continuous  line  passes  represent  the  means  of 
the  rows.  Each  asterisk  represents  a  subject. 


with  an  increase  in  x-values  from  the  fiftieth  percentile  up.  Be¬ 
low  this  point  there  is  little  relation  between  y  and  x-values.25 

The  relation  between  unclassified  errors  and  the  criterion  is 
shown  in  Table  IX.  The  agreement  between  the  regression  of 
the  x-values  on  y  and  the  y-values  on  x  is  not  close.  In  neither 
case  is  the  tendency  for  one  value  to  increase  with  an  increase 
in  the  other  constant.  The  x-values  increase  with  an  increase 
in  y-values  from  the  fortieth  percentile  up  to  the  sixtieth.  The 
other  regression  line  is  almost  horizontal  from  the  thirtieth  to 
the  sixtieth  percentile.  An  increase  in  Binet-Simon  scores  in¬ 
dicates  nothing  with  respect  to  unclassified  errors  until  the  for¬ 
tieth  percentile  is  reached.  An  increase  in  Binet-Simon  scores 


25  Reasons  for  this  lack  of  relation  in  the  lower  quartile  will  be  suggested 
later  in  comparing  the  final  scores  with  the  criterion. 


22 


B.  F.  H AUGHT 


Table  IX.  Showing  the  Distribution  of  Subjects  on  the  Basis  of  Unclassi¬ 
fied  Errors  in  Rational  Learning  and  the  Binet-Simon  Tests.  Circles 
through  which  the  broken  line  passes  represent  the  means  of  the 
columns  and  those  through  which  the  continuous  line  passes  represent 
the  means  of  the  rows.  Each  asterisk  represents  a  subject. 


from  the  fortieth  to  the  sixtieth  percentile  means  a  rather  rapid 
increase  in  unclassified  errors.  Above  the  sixtieth  percentile  an 
increase  in  Binet-Simon  scores  means  no  change  in  unclassified 
errors.  From  the  beginning  to  the  end,  an  increase  in  unclassified 
errors  means  nothing  with  respect  to  intelligence  as  measured 
by  the  Binet-Simon  Tests. 

Table  X  shows  the  relation  existing  between  logical  errors 
and  the  criterion.  The  agreement  between  the  two  sets  of 
values  is  not  close.  There  is  a  fairly  constant  increase  in  y-values 
with  an  increase  in  x-values  from  the  fortieth  percentile  up. 
A  smoothed  curve  will  show  an  increase  from  the  very  be¬ 
ginning.  In  the  other  regression  line  there  is  no  tendency  for 
the  x-values  to  increase  constantly.  Up  to  the  fortieth  percentile 
an  increase  in  Binet-Simon  scores  means  no  change  in  score  in 


INTERRELATION  OF  HIGHER  LEARNING  PROCESSES  23 

Table  X.  Showing  the  Distribution  of  Subjects  on  the  Basis  of  Logical 
Errors  in  Rational  Learning  and  the  Binet-Simon  Tests.  Circles 
through  which  the  broken  line  passes  represent  the  means  of  the 
columns  and  those  through  which  the  continuous  line  passes  represent 
the  means  of  the  rows.  Each  asterisk  represents  a  subject. 


logical  errors,  but  from  here  on  to  the  sixty- fifth  percentile,  it 
means  a  constant  increase.  Above  this  point  there  are  only  five 
cases,  and  the  curve  has  no  significance. 

The  skewness  of  each  distribution  is  almost  zero,  since  the 
median  and  the  mean  almost  coincide  when  the  scores  are  reduced 
to  percentiles.  This  assumes  that  skewness  is  measured  in  terms 
of  the  median,  the  mean,  and  the  standard  deviation.  All  medians 
and  means  are  approximately  50,  and  all  standard  deviations  are 
approximately  16.66. 

VI.  The  Rational  Learning  Test  ( Modified ) 

(1)  Description  of  Test  and  Method  of  Scoring. 

This  test  is  very  similar  to  Rational  Learning.  The  apparatus 
consists  of  a  board  about  twenty  inches  sguare,  through  which 


24 


B.  F.  H AUGHT 


are  put  one  hundred  bolts  arranged  in  ten  rows  with  ten  bolts 
in  a  row.  The  rows  are  lettered  from  A  to  J  and  the  bolts  in 
each  are  numbered  I  to  io.  One  bolt,  and  only  one,  in  each 
row  is  connected  in  a  circuit  with  an  electric  bell  so  that  when 
this  bolt  is  touched  with  a  stylus  the  bell  will  ring.  Figure  I 
shows  the  apparatus. 

Fig.  I.  Showing  Apparatus  for  Rational  Learning  (Modified). 


J 

* 

* 

* 

* 

* 

* 

* 

* 

* 

* 

I 

* 

* 

♦ 

* 

* 

* 

* 

* 

* 

* 

H 

* 

* 

* 

* 

* 

* 

* 

* 

* 

* 

G 

* 

* 

* 

* 

* 

* 

* 

* 

* 

* 

F 

* 

* 

♦ 

* 

* 

* 

* 

* 

* 

* 

E 

* 

* 

* 

* 

* 

* 

* 

* 

* 

* 

D 

* 

* 

* 

* 

* 

* 

* 

* 

♦ 

* 

C 

* 

* 

* 

* 

* 

* 

* 

* 

♦ 

* 

B 

* 

* 

* 

♦ 

* 

* 

* 

* 

* 

* 

A 

* 

* 

* 

* 

* 

* 

* 

* 

* 

* 

i 

2 

3 

4 

5 

6 

7 

8 

9 

IO 

Each  asterisk  represents  a  bolt.  The  bolts  are  actually  num¬ 
bered  in  each  row  just  as  indicated  in  row  A  in  the  diagram. 
The  method  of  recording  the  data  is  exactly  as  in  Rational  Learn¬ 
ing.  The  instructions  to  the  subject  follow : 

“You  have  in  the  apparatus  before  you  ten  rows  of  bolts  with 
ten  bolts  in  each  row.  The  rows  are  lettered  from  A  to  J  and 
the  bolts  in  each  row  are  numbered  from  i  to  io.  One  bolt  in 
each  row,  and  only  one,  is  connected  in  such  a  way  that  the 
bell  will  ring  when  the  circuit  is  made.  That  is,  each  letter  is 
assigned  a  number  in  a  random  order  from  i  to  io.  This  num¬ 
ber  is  the  one  that  will  cause  the  bell  to  ring  when  the  bolt  is 
touched.  No  two  letters  have  the  same  number. 

Your  problem  is  to  begin  with  row  A  and  find  the  bolt  that 
will  ring  the  bell.  Then  go  on  to  row  B  and  find  the  bolt.  Con¬ 
tinue  until  you  have  reached  row  J.  Now  go  back  to  row  A  and 
repeat  the  process.  Continue  repeating  the  process  until  you 
go  from  A  to  J  twice  in  succession  without  making  any  mistake. 
Then  you  are  through. 


INTERRELATION  OF  HIGHER  LEARNING  PROCESSES  25 


You  are  to  ask  no  questions  after  you  start,  but  are  to  use  all 
the  mental  powers  at  your  command  in  order  to  complete  the 
learning  as  soon  as  possible.  You  will  be  judged  by  (1)  the 
total  time  you  take,  (2)  the  number  of  errors  or  wrong  guesses 
you  make  (every  bolt  you  touch  being  a  guess),  (3)  the  number 
of  repetitions  from  A  to  J  that  you  require  for  the  learning. 
Re-read  these  instructions  carefully,  if  necessary,  to  understand 
what  you  are  to  do.  The  meaning  will  be  clearer  as  we  go  on 
with  the  experiment/' 

The  subject  stood  facing  the  apparatus  so  that  row  A  was  to¬ 
ward  him.  The  experimenter  recorded  every  response  just  as 
was  done  in  Rational  Learning.  When  the  test  was  finished  the 
total  time  was  recorded  and  the  subject  was  asked  to  write  as 
much  as  he  could  about  the  method  he  used  in  learning  the 
problem. 

The  same  three  schedules  of  numbers  were  used  in  this  test  as 
in  Rational  Learning.26  Those  having  schedule  1  in  Rational 
Learning  had  schedule  2  in  this  one;  those  having  schedule  3, 
had  1 ;  and  those  having  schedule  2,  had  3.  The  same  precau¬ 
tion  was  taken  to  prevent  coaching  as  in  Rational  Learning. 
Each  subject  was  asked  not  to  tell  any  other  member  of  the  class 
anything  that  might  assist  in  the  learning.  Results  are  given 
in  Table  XI. 

Table  XII  shows  that  time  has  something  in  common  with 
the  criterion  that  is  not  common  to  the  other  factors.  Perseve- 
rative  errors  seem  to  be  least  significant  and  may  be  dropped  as 
far  as  the  final  scores  are  concerned.  If  we  consider  only  the 
four  factors  and  partial  correlations  of  the  third  order,  logical 
errors  appear  useless.  In  like  manner,  when  the  three  remain¬ 
ing  factors  are  considered  alone,  repetitions  appear  insignificant. 
If  we  push  the  analysis  further,  however,  it  is  very  evident  that 
unclassified  errors  must  be  retained  with  time  to  make  up  the 
final  score.  We  may  make  the  analysis  more  logical  by  first 
considering  ri6  2345  =  .01,  which  means  that  there  is  nothing  com¬ 
mon  to  1  and  6  that  is  not  contained  in  2,  3,  4,  and  5.  Factor  6 
may  therefore  be  dropped.  In  like  manner,  since  ^5.234  *03 

26  This  test  was  given  before  Rational  Learning. 


26 


B.  F.  H AUGHT 


Table  XI.  Showing  the  Number  of  Minutes,  the  Number  of  Repetitions, 
the  Number  of  each  Kind  of  Errors,  and  the  Percentile  Rank  for 
Each  Kind  of  Data  in  Rational  Learning  (Modified). 


Subject 

Raw  Score  in 

|  Time 

|  Rep. 

j  Uc.E. 

L.E. 

P.E. 

I 

3 

4 

47 

19 

O 

2 

7 

10 

138 

72 

3 

3 

7 

4 

42 

18 

3 

4 

10 

7 

55 

17 

3 

5 

2 

3 

45 

l6 

0 

6 

11 

7 

70 

24 

3 

7 

9 

10 

102 

l6 

13 

8 

18 

12 

182 

67 

21 

9 

27 

10 

124 

60 

8 

IO 

15 

9 

130 

6l 

5 

ii 

13 

13 

H5 

58 

9 

12 

10 

9 

69 

23 

0 

13 

10 

12 

164 

90 

5 

14 

11 

10 

142 

58 

11 

15 

10 

7 

67 

37 

2 

16 

4 

4 

59 

23 

0 

1 7 

1 7 

18 

261 

94 

16 

18 

10 

7 

66 

27 

15 

19 

7 

10 

145 

66 

4 

20 

16 

16 

176 

72 

22 

21 

12 

8 

128 

79 

6 

22 

7 

7 

95 

55 

1 

23 

1 7 

15 

167 

83 

2 

24 

6 

3 

48 

22 

3 

25 

15 

12 

114 

38 

11 

26 

6 

6 

73 

22 

2 

27 

9 

9 

92 

48 

6 

28 

9 

7 

1 16 

67 

5 

29 

i  n 

!  i° 

124 

50 

8 

30 

7 

7 

43 

26 

2 

31 

28 

12 

165 

83 

24 

32 

19 

12 

123 

55 

10 

33 

14 

16 

207 

141 

15 

34 

12 

10 

118 

65 

3 

35 

23 

14 

217 

122 

47 

36 

29 

14 

236 

no 

14 

37 

10 

9 

106 

49 

2 

38 

18 

14 

314 

152 

30 

39 

5 

3 

25 

4 

0 

40 

13 

10 

127 

58 

10 

41 

11 

10 

74 

26 

4 

42 

9 

12 

73 

23 

0 

43 

12 

11 

no 

54 

13 

44 

23 

15 

292 

153 

24 

45 

19 

6 

78 

34 

6 

46 

11 

7 

85 

49 

3 

47 

18 

16 

231 

109 

11 

48 

15 

8 

7i 

29 

8 

49 

12 

15 

109 

44 

18 

Percentile  Rank  in 


Time 

Rep. 

Uc.E.  j 

L.E.  j 

P.E.  | 

ScoreJ 

82 

75 

75 

69 

76 

79 

68 

5i 

43 

41 

58 

56 

68 

75 

82 

71 

58 

77 

57 

65 

69 

73 

58 

67 

87 

82 

77 

76 

76 

85 

53 

65 

63 

63 

58 

59 

61 

51 

53 

7  6 

38 

58 

37 

42 

35 

43 

28 

35 

18 

5i 

46 1 

46 

46  1 

32 

43 

56 

44 

1  46 

53 

43 

46 

39 

49 

48 

45 

48 

57 

56 

64 

65 

76 

61 

57 

42 

40 

33 

53 

49 

53 

5i 

42 

48 

4i 

48 

57 

65 

65 

58 

63 

64 

79 

75 

68 

65 

76 

73 

40 

16 

21 

32 

34 

29 

57 

65 

65 

61 

36 

61 

68 

5i 

42 

43 

55 

55 

4i 

27 

35 

4i 

25 

38 

49 

59 

45 

38 

5i 

46 

68 

65 

54 

49 

68 

64 

40 

33 

38 

35 

63 

40 

74 

82 

73 

67 

58 

73 

43 

42 

50 

57 

4i 

46 

74 

70 

61 

67 

63 

70 

61 

56 

55 

54 

5i 

59 

61 

65 

49 

43 

53 

55 

53 

5i 

46 

52 

46 

49 

68 

65 

79 

62 

63 

73 

14 

42 

39 

35 

21 

23 

33 

42 

47 

49 

43 

40 

45 

27 

32 

18 

36 

39 

49 

5i 

48 

44 

58 

49 

24 

37 

30 

21 

0 

25 

0 

37 

25 

26 

37 

0 

57 

56 

52 

53 

63 

54 

37 

37 

0 

14 

14 

14 

77 

82 

87 

87 

76 

85 

46 

5i 

45 

48 

43 

45 

53 

5i 

5i  , 

62 

55 

53 

61  | 

42  | 

61  | 

65  1 

76 1 

64 

49 

46 

51 

50 

38 

5i 

24 

33 

14 

0 

21 

18 

33 

70 

59 

59 

5i 

45 

53 

65 

58 

53 

58 

56 

37 

27 

28 

28 

4i 

33 

43 

59 

62 

60 

46 

53 

49 

33 

51 

54 

3i 

5i 

INTERRELATION  OF  HIGHER  LEARNING  PROCESSES  27 


Table  XI  (Continued) 


Subject 

Rav\ 

1  Score  in 

Percentile  Rank  in 

Time 

Rep. 

Uc.E. 

■  ■ 

1 

L.E. 

P.E. 

Time 

Rep. 

Uc.E. 

L.E. 

P.E. 

ScoreJ 

50 

7 

8 

95 

52 

6 

68 

59 

54 

52 

51 

64 

51 

24 

12 

250 

no 

17 

21 

42 

23 

26 

32 

21 

52 

21 

17 

189 

7 1 

24 

28 

21 

33 

42 

21 

29 

53 

12 

10 

154 

87 

12 

49 

5i 

40 

34 

39 

44 

54 

12 

8 

48 

8 

2 

49 

59 

73 

79 

63 

64 

55 

19 

11 

235 

95 

21 

33 

46 

27 

30 

28 

27 

56 

17 

14 

172 

78 

7 

40 

37 

36 

38 

49 

38 

57 

9 

8 

131 

62 

0 

61 

59 

43 

45 

76 

53 

53 

13 

18 

269 

11 7 

16 

46 

16 

18 

23 

34 

32 

59 

19 

15 

151 

83 

2 

33 

33 

4i 

35 

63 

36 

60 

15 

16 

207 

74 

19 

43 

27 

32 

40 

30 

37 

61 

13 

13 

59 

5 

16 

46 

39 

68 

82 

34 

58 

62 

9 

8 

100 

43 

7 

61 

59 

54 

55 

49 

58 

63 

19 

15 

166 

81 

11 

33 

33 

38 

37 

4i 

34 

64 

19 

12 

91 

29 

7 

33 

42 

56 

60 

49 

44 

65 

11 

11 

122 

76 

1 

53 

46 

48 

39 

68 

5i 

66 

19 

9 

105 

4i 

2 

33 

56 

52 

56 

63 

42 

67 

14 

16 

167 

64 

9 

45 

27 

38 

45 

45 

42 

68 

7 

11 

88 

37 

6 

68 

46 

58 

58 

5i 

67 

69 

12 

11 

104 

53 

11 

49 

46 

53 

5i 

4i 

52 

70 

7 

10 

61 

20 

2 

68 

5i 

66 

68 

63 

69 

7 1 

1 7 

24 

188 

94 

9 

40 

0 

34 

32 

45 

36 

72 

22 

7 

9i 

41 

4 

27 

65 

56 

56 

55 

42 

73 

8 

10 

88 

52 

1 

64 

5i 

58 

52 

68 

64 

74 

8 

6 

52 

18 

0 

64 

70 

70 

7i 

76 

69 

f  Scores  are  found  by  adding,  the  percentile  rank  in  time  to  the  percentile 
rank  in  unclassified  errors  and  then  again  reducing  to  absolute  percentiles  by 
Rugg’s  table.  The  reason  for  this  will  appear  later. 


Table  XII.  Showing  Correlations  and  Partial  Correlations  of  Each  Factor]* 
of  Rational  Learning  (Modified)  with  the  Binet-Simon  Tests. 


12 

.42 

13 

•3i 

14 

•44 

15 

42 

16 

•35 

12-3 

.31 

132 

.08 

14-2 

.24 

15-2 

•23 

16-2 

.11 

124 

.19 

13-4 

—.05 

14-3 

•33 

15-3 

•30 

16-3 

.21 

12-5 

.23 

13  5 

.04 

14-5 

-15 

15-4 

.04 

164 

.07 

12-6 

.27 

13-6 

-13 

14-6 

.29 

15-6 

.28 

16-5 

.12 

12-34 

.20 

13-24 

.08 

14-23 

.24 

15-23 

.21 

16-23 

.08 

12.35 

•23 

1325 

—.04 

14-25 

.08 

15-24 

.04 

16-24 

.00 

1236 

.24 

13-26 

.04 

14-26 

.20 

15-26 

.20 

16-25 

.04 

12-45 

•  19 

13-45 

—  05 

14-35 

-15 

15-34 

.04 

i6-34 

.07 

12-46 

.17 

13-46 

— .06 

I4-36 

.27 

15-36 

•25 

16-35 

.12 

12-56 

-19 

I3-56 

.00 

I4-56 

.10 

I5-46 

-05 

16-45 

.07 

12-345 

.20 

13-245 

— .08 

14-235 

.11 

15-234 

•03 

16-234 

.01 

12-346 

.19 

13-246 

— .09 

14236 

.23 

15-236 

.20 

16-235 

.04 

12-356 

.19 

13-256 

—.05 

14-256 

.07 

15-246 

.04 

16-245 

.01 

12-456 

•17 

I3-456 

—.05 

I4-356 

.11 

I5-346 

.04 

16 -345 

.08 

12-3456 

.19 

13-2456 

— .08 

I4-2356 

.10 

15-2346 

.03 

16-2345 

.01 

fFor  the  sake  of  brevity  the  factors  are  designated  by  numbers  as  follows : 

1.  Binet-Simon  Tests  4.  Unclassified  Errors 

2.  Time  5.  Logical  Errors 

3.  Repetitions  6.  Perseverative  Errors 


28 


B.  F.  H AUGHT 


factor  5  may  be  discarded.  Since  r13.24  =  .08,  factor  3  may  be 
discarded.  But  since  r12.4  =  .19,  and  r14.2  =  .24,  it  is  evident 
that  factors  2  and  4  must  be  retained. 

This  conclusion  may  be  further  verified  by  using  multiple 
correlation.  The  following  results  are  found : 

R-i (23456)  ~  -479 
RiG*)  =  473 

It  is  seen  from  the  above  that  very  little  is  lost  by  excluding  all 
the  factors  except  time  and  unclassified  errors.  We  shall  use 
for  our  final  scores,  then,  these  two  factors  which  appear  to 
give  everything  that  is  necessary  to  get  the  highest  correlation 
with  the  criterion. 

Our  next  problem  is  to  find  the  combination  of  time  and  un¬ 
classified  errors  that  will  give  this  best  correlation.  The  same 
formulae  will  be  used  as  were  used  in  Rational  Learning.  Desig¬ 
nating  unclassified  errors  by  M  and  time  by  m,  we  may  use  the 
following  data  for  finding  the  best  value  of  C  and  the  resulting 
correlation : 


r 


IM 


r 


Im 


r 


Mm 


=  44 
=  .42 

=  .66 


When  these  values  are  substituted  in  formula  (2),  the  value  of 
C  is  found  to  be  .79.  This  means  that  the  best  combination  of 
time  and  unclassified  errors  is  to  add  .79  of  the  time  to  the  un¬ 
classified  errors.  This  gives  a  correlation  of  .47;  but  if  1  is  used 
in  the  formula  instead  of  .79,  the  correlation  is  still  .47.  For 
our  final  score  in  this  test,  we  shall  use  time  and  unclassified  errors 
combined  equally.  The  exact  method  of  getting  them  will  be 
to  add  together  the  scores  in  time  and  unclassified  errors  and 
then  reduce  to  absolute  percentiles  by  the  same  method  as  was  used 
in  Rational  Learning. 

(2)  Analysis  of  Data. 

There  is  a  “present  but  low”  positive  correlation  between  the 


INTERRELATION  OF  HIGHER  LEARNING  PROCESSES  29 

criterion  and  repetitions  and  between  the  criterion  and  per- 
severative  errors.  The  correlation  of  the  criterion  with  each  of 
the  other  factors  is  “marked/  Subjects  above  the  average  in 
the  former  will  tend  to  be  above  the  average  in  each  of  the  latter. 
Since  the  variability^'  is  made  the  same  in  each  kind  of  data  by 
reducing  to  absolute  percentiles,  a  unit-change  in  one  test  or  fac¬ 
tor  will  be  accompanied  by  a  like  change  in  the  other  test  or 
factor  equal  to  the  correlation  of  the  two  factors.  Thus  time  and 
the  criterion  have  a  correlation  of  .42.  Therefore  every  unit- 
change  in  one  will  be  accompanied  by  .42  of  a  unit-change  in  the 
other.  In  like  manner,  each  of  the  other  factors  may  be  com¬ 
pared  with  the  criterion  by  reference  to  the  correlations  in  Table 
XII. 

Each  factor  in  this  test  has  much  in  common  with  the  criterion. 
Unclassified  errors  have  most  and  repetitions  least.  Table  XII 


Table  XIII.  Showing  Correlations  and  Partial  Correlations  of  the  Factors 

in  the  Rational  Learning  Test  (Modified). 


23 

.60 

24 

.66 

25 

.61 

26 

-65 

34 

•77 

23-4 

.19 

24-3 

-39 

25-3 

.36 

26  3 

•45 

34-2 

.62 

23-5 

•33 

24-5 

•32 

254 

.01 

26-4 

•35 

34-5 

•53 

23-6 

•34 

24-6 

.38 

25-6 

•36 

26-5 

■45 

34-6 

.61 

23-45 

.20 

24-35 

.18 

25-34 

.05 

26-34 

•33 

34-25 

•47 

23-46 

.15 

24-36 

.23 

2536 

.24 

26.35 

.38 

34-26 

•55 

23  56 

.21 

24-56 

.14 

25-46 

.07 

26.45 

•36 

34-56 

•45 

23-456 

.16 

24-356 

.06 

25-346 

.09 

26-345 

•34 

34-256 

.42 

35 

.67 

36 

.61 

45 

.92 

46 

.70 

56 

.60 

35-2 

.48 

36-2 

■36 

45-2 

.87 

46-2 

.48 

56-2 

•34 

35-4 

— .16 

36-4 

.16 

45-3 

-85 

46-3 

•45 

56-3 

•33 

35-6 

.48 

36-5 

-35 

45-6 

.87 

46-5 

•47 

56-4 

—•15 

35-24 

— .16 

36-24 

.10 

45-23 

.83 

46-23 

•34 

56-23 

.20 

35-26 

.41 

36-25 

.24 

45-26 

.85 

46-25 

•39 

56-24 

—.17 

35-46 

—.13 

36-45 

.14 

45-36 

.83 

46-35 

•35 

56-34 

—.13 

35-246 

—.14 

36-245 

.07 

45-236 

.82 

46-235 

•32 

56-234 

— .16 

shows  that  time  contains  all  that  is  common  to  repetitions  and 
the  criterion  and  nearly  all  that  is  common  to  perseverative  errors 
and  the  criterion.  Unclassified  errors  contain  all  that  is  common 
to  the  criterion  and  any  one  of  the  three  factors,  repetitions, 
logical  errors  and  perseverative  errors.  Uogical  errors  contain 
all  that  is  common  to  repetitions  and  the  criterion. 

27  The  standard  deviations  for  time,  repetitions,  unclassified  errors,  logical 
errors,  and  perseverative  errors  are  16.65,  16.48,  16.59,  16.68,  and  16.35  re¬ 
spectively. 


30 


B.  F.  H AUGHT 


Table  XIII  shows  that  the  factors  have  a  “high"  correlation 
with  each  other.  Unclassified  and  logical  errors  have  the  highest. 
Since  the  correlation  of  these  two  factors  is  so  high,  neither  of 
them  can  have  very  much  that  is  not  in  the  other. 

Table  XIV.  Showing  the  Distribution  of  Subjects  on  the  Basis  of  Time  in 
Rational  Learning  (Modified)  and  the  Binet-Simon  Tests.  Circles 
through  which  the  broken  line  passes  represent  the  means  of  the 
columns,  and  those  through  which  the  continuous  line  passes  repre¬ 
sent  the  means  of  the  rows.  Each  asterisk  represents  a  subject. 


The  several  correlation-ratios  for  each  of  the  factors  with  the 
criterion  are  as  follows : 

12  =  .56  and  .66 

13  =  .47  and  .59 

14  =  .53  and  .61 

15  =  .58  and  .60 

16  =  .49  and  .49 


INTERRELATION  OF  HIGHER  LEARNING  PROCESSES 


3i 


The  Blakeman  formula  gives  results  as  follows: 


Tests  1  and  2, 
Tests  1  and  3, 
Tests  1  and  4, 
Tests  1  and  5, 
Tests  1  and  6, 


2.36  and  3.24 
2.25  and  3.20 
1.87  and  2.69 
2.55  and  2.73 
2.19  and  2.19 


All  the  correlations  are  non-linear  except  the  last  one,  the  crit¬ 
erion  and  perseverative  errors. 

Table  XIV  shows  the  correspondence  between  scores  in  time 
and  the  criterion.  The  Blakeman  formula  indicates  that  each  of 
the  regression  lines  is  non-linear.  The  curve  of  the  means  of 
the  rows  shows  very  little  change  in  x-values  with  an  increase  in 
y-values  up  to  the  fifty-fifth  percentile,  where  the  change  is 
accelerated,  probably,  on  account  of  the  fact  that  the  Binet-Simon 


Table  XV.  Showing  the  Distribution  of  subjects  on  the  Basis  of  Repe¬ 
titions  in  Rational  Learning  (Modified)  and  the  Binet-Simon  Tests. 
Circles  through  which  the  broken  line  passes  represent  the  means 
of  the  columns,  and  those  through  which  the  continuous  line  passes 
represent  the  means  of  the  rows.  Each  asterisk  represents  a  subject. 


32 


B.  F.  H AUGHT 


tests  do  not  actually  test  the  brightest  subjects.  The  curve  of 
the  means  of  the  columns  has  four  distinct  parts.  As  the  x-values 
increase,  the  y-values  decrease  rapidly  from  the  twenty-fifth  to 
the  thirty-fifth  percentile,  increase  rapidly  from  the  thirty-fifth 
to  the  forty-fifth  percentile,  remain  about  the  same  from  the 
forty-fifth  to  the  sixty-fifth  percentile,  and  increase  rapidly  from 
the  sixty-fifth  percentile. 

Table  XV  shows  the  correspondence  between  the  scores  in 
repetitions  and  the  criterion.  The  regression  line  of  the  means 
of  the  columns  may  be  considered  linear  according  to  the  Blake- 
man  test.  The  regression  line  of  the  means  of  the  rows,  how¬ 
ever,  is  non-linear.  The  non-linearity  is  caused  by  the  four  cases 
in  the  second  and  third  rows  from  the  botton  and  the  one  case 
in  the  top  row.  The  removal  of  these  five  cases  will  reduce  the 


Table  XVI.  Showing  the  Distribution  of  Subjects  on  the  Basis  of  Un¬ 
classified  Errors  in  Rational  Learning  (Modified)  and  the  Binet- 
Simon  Tests.  Circles  through  which  the  broken  line  passes  represent 
the  means  of  the  columns  and  those  through  which  the  continuous 
line  passes  represent  the  means  of  the  rows.  Each  asterisk  represents 
a  subject. 


x  s Unclassified  Errors  in  Rational  Learning 


0- 

/? 

20- 

24 

25- 

Zf 

30- 

31- 

35- 

?? 

40- 

44 

45- 

49 

5°- 

5+ 

55- 

?,? 

60- 

65- 

6? 

70- 

74- 

75- 

7? 

80- 

\00 

100- 

60 

-O* 

1 

75- 

75 

■# 

*#■ 

* 

4 

74- 

70 

0 

% 

» 

♦ 

*» 

*  / 

Q* 

*> 

A 

8 

% 

* 

•» 

P 

» 

„  6 

59- 

55 

* 

»» 

o 

»• 

n 

/ 

-  \ 

/ 

$ 

i 

i 

k 

> 

% 

6 

54- 

50 

« 

* 

* 

/§r 

/ 

k  / 

V  i 

»* 

\  • 

'6 

6 

10 

49- 

45 

** 

#■ 

* 

A- 

* 

'ft/ 

** 

k 

*■ 

* 

11 

44- 

40 

* 

ft* 

♦ 

* 

5 

35- 

55 

V 

\ 

*\ 

1 

/ 

/ 

$ 

»  

*  C 

* 

*♦ 

7 

34- 

30 

-o;' 

-O 

* 

* 

7 

29- 

25 

JPT 

2 

24- 

20 

-oc 

< 

- 

2 

,si 

* 

3 

3 

2 

3 

5 

7 

8 

9 

n 

7 

5 

6 

3 

3 

2 

74 

«« 

£ 

s: 

o 

•$ 


INTERRELATION  OF  HIGHER  LEARNING  PROCESSES  33 


Table  XVII.  Showing  the  Distribution  of  Subjects  on  the  Basis  of  Logical 
Errors  in  Rational  Learning  (Modified)  and  the  Binet-Simon  Tests. 
Circles  through  which  the  broken  line  passes  represent  the  means  of 
the  columns  and  those  through  which  the  continuous  line  passes 
represent  the  means  of  the  rows.  Each  asterisk  represents  a  subject. 


Logical  Errors  in  Rational  L  earning  (Modified) 


correlation-ratio  from  .59  to  -34>  provided  the  mean  and  standard 
deviation  are  not  changed.  Such  a  reduction  in  correlation-ratio 
will  destroy  the  non-linearity. 

Table  XVI  shows  the  correspondence  between  the  scores  in 
unclassified  errors  and  the  criterion.  The  regression  line  of  the 
means  of  the  columns  is  linear  according  to  the  test.  The  other 
regression  line,  however,  is  non-linear.  The  non-linearity  can 
be  eliminated  by  removing  the  two  cases  in  the  second  row  from 
the  bottom.  The  same  result  can  be  obtained  by  assuming  that 

these  two  cases  fall  on  the  median. 

Table  XVII  shows  the  correspondence  between  the  scores  in 
logical  errors  and  the  criterion.  Here  both  regression  lines  are 
slightly  non-linear.  The  non-linearity,  however,  is  due  to  a  few 
cases  and  for  that  reason  has  no  significance. 


34 


B.  F.  H AUGHT 


VII.  Checker  Puzzle 

(i)  Description  of  Test  and  Method  of  Scoring. 

This  may  be  called  a  checker  puzzle  test  because  of  its  similar¬ 
ity  to  the  game  of  checkers.  As  far  as  the  writer  knows  it  was 
first  used  as  a  psychological  experiment  by  Dr.  Strong  in  the 
Jesup  Psychological  Laboratory  of  George  Peabody  College 
for  Teachers.  He  also  gives  a  suggestion  for  its  use  in  the 
Psychological  Bulletin.28  The  instructions  to  the  subject  and 
the  method  of  scoring  are  different  in  many  respects  from  those 
used  in  the  Jesup  Psychological  Laboratory.  They  were  de¬ 
vised  by  the  writer,  but,  of  course,  reflect  to  a  considerable  de¬ 
gree  those  with  which  he  was  already  acquainted. 


Fig.  II.  Showing  Apparatus  Used  in  the  Checker  Puzzle  Test. 


The  subject  is  given  a  card  on  which  are  seven  circles  as 
shown  in  Figure  II.  He  is  also  given  three  red  and  three  black 
checkers.  The  instructions  to  the  subject  are  as  follows: 

“You  are  here  given  a  row  of  seven  circles.  The  three  at  the 
left  are  red,  the  three  at  the  right  are  black,  and  the  middle  one 
is  black  on  the  right  half  and  red  on  the  left  half.  You  are  also 
given  three  red  and  three  black  checkers.  You  are  to  place  the 
three  red  checkers  on  the  three  black  circles  and  the  three  black 
checkers  on  the  three  red  circles. 

“Your  problem  is  to  get  the  three  red  checkers  on  the  three  red 
circles  and  the  three  black  checkers  on  the  three  black  circles. 
You  must  move  but  one  checker  at  a  time,  jump  only  one  at  a 
time,  and  never  move  backwards.  When  you  are  blocked  so  that 
you  cannot  move  farther,  set  the  checkers  back  to  the  starting 
point  and  begin  anew.  When  you  can  go  through  the  problem 
three  times  in  succession  without  any  errors,  we  will  consider 

28  Strong,  E.  K.,  Jr.,  The  Learning  Process,  “ Psychol .  Bull.,  1918,  XV, 
328  ff. 


INTERRELATION  OF  HIGHER  LEARNING  PROCESSES  35 

it  learned.  Keep  in  mind  that  your  results  are  being  judged  (i) 
by  the  time  spent,  (2)  by  the  number  of  attempts  (each  time  you 
begin  counting  an  attempt,  whether  you  are  successful  or  not), 
(3)  by  the  number  of  successful  solutions  required  for  the  learn¬ 
ing.” 

The  subject  sat  at  one  side  of  the  table  and  the  experimenter 
at  the  other.  The  latter  kept  an  accurate  account  of  the  time, 
the  number  of  attempts,  and  the  number  of  successful  solutions. 
The  results  are  found  in  Table  XVIII. 


Table  XVIII.  Showing  the  Number  of  Minutes,  the  Number  of  Attempts, 
the  Number  of  Solutions,  and  the  Percentile  Rank  for  Each  Kind 
of  Data  in  the  Checker  Puzzle  Test. 


Subject 

Score 

in 

Percen 

Rank 

tile 

in 

Subject 

Score 

in 

Percentile 
Rank  in 

T 

A 

1  s 

T 

A 

S 

T 

A 

S 

T 

A 

S 

1 

9 

11 

4 

74 

15 

78 

38 

19 

30 

12 

53 

39 

25 

2 

16 

15 

6 

58 

63 

59 

39 

8 

7 

5 

81 

86 

69 

3 

17 

23 

9 

56 

5i 

40 

40 

9 

8 

6 

74 

82 

59 

4 

26 

14 

6 

4i 

65 

59 

4i 

14 

16 

6 

61 

61 

59 

5 

12 

20 

8 

67 

54 

46 

42 

13 

17 

6 

64 

59 

59 

6 

22 

18 

6 

49 

58 

59 

43 

18 

16 

10 

55 

61 

35 

7 

26 

14 

3 

41 

65 

86 

44 

19 

30 

6 

53 

39 

59 

8 

3i 

28 

9 

35 

43 

40 

45 

13 

12 

8 

64 

70 

46 

9 

16 

18 

8 

58 

58 

46 

46 

25 

27 

8 

45 

44 

46 

10 

29 

24 

7 

38 

48 

52 

47 

30 

25 

7 

37 

46 

52 

11 

29 

29 

6 

38 

42 

59 

48 

58 

57 

9 

14 

18 

40 

12 

11 

14 

5 

69 

65 

69 

49 

24 

30 

6 

45 

39 

59 

13 

19 

32 

6 

53 

36 

59 

50 

52 

49 

11 

19 

25 

3i 

14 

10 

12 

6 

70 

70 

59 

51 

52 

49 

11 

19 

25 

3i 

15 

21 

25 

15 

5i 

46 

52 

52 

12 

19 

7 

67 

56 

52 

16 

29 

23 

6 

38 

5i 

59 

53 

21 

30 

8 

5i 

39 

46 

17 

23 

24 

9 

47 

48 

40 

54 

24 

25 

5 

45 

46 

69 

18 

20 

10 

8 

52 

77 

46 

55 

26 

37 

11 

4i 

34 

31 

19 

19 

23 

7 

53 

5i 

52 

56 

4i 

52 

14 

23 

21 

0 

20 

35 

45 

9 

33 

28 

40 

57 

8 

13 

5 

81 

67 

69 

21 

13 

9 

6 

64 

79 

59 

58 

14 

16 

5 

61 

61 

69 

22 

22 

30 

12 

49 

39 

25 

59 

25 

33 

13 

43 

35 

16 

23 

9 

23 

6 

74 

5i 

59 

60 

35 

4i 

10 

33 

30 

35 

24 

35 

23 

8 

33 

5i 

46 

61 

25 

21 

8 

43 

53 

46 

25 

36 

46 

13 

29 

27 

16 

62 

16 

19 

5 

58 

56 

69 

26 

6 

12 

8 

86 

70 

46 

63 

37 

29 

8 

25 

42 

46 

27 

12 

19 

4 

67 

56 

78 

64 

19 

16 

4 

53 

61 

78 

28 

17 

28 

8 

56 

43 

46 

65 

15 

39 

8 

60 

32 

46 

29 

30 

23 

6 

37 

5i 

59 

66 

9 

21 

5 

69 

53 

69 

30 

13 

12 

8 

64 

70 

46 

67 

28 

12 

10 

40 

70 

35 

3i 

36 

31 

10 

29 

37 

35 

68 

12 

18 

8 

67 

58 

46 

32 

24 

25 

6 

45 

46 

59 

69 

36 

62 

11 

29 

14 

3i 

33 

23 

20 

9 

47 

54 

40 

70 

23 

32 

9 

47 

36 

40 

34 

36 

38 

7 

29 

33 

52 

7i 

62 

80 

12 

0 

0 

25 

35 

21 

23 

9 

51 

5i 

40 

72 

15 

13 

4 

60 

67 

78 

36 

23 

27 

10 

47 

44 

35 

73 

16 

17 

7 

58 

59 

52 

27 

21 

40 

12 

51 

3i 

25 

74 

33 

23 

6 

35 

5i 

59 

36 


B.  F.  H AUGHT 


Table  XIX.  Showing  Correlations  and  Partial  Correlations  of  Each  Factor* 
of  the  Checker  Puzzle  with  the  Binet-Simon  Test  and  with  Each 
Other. 


12 

.26 

13 

.18 

14 

.20 

12-3 

.18 

13-2 

•03 

14-3 

.06 

12-4 

.19 

13-4 

.05 

14-2 

.08 

12-34 

.18 

13-24 

—.03 

14-23 

.06 

23 

.62 

24 

•5i 

34 

.76 

23-4 

.41 

24-3 

.08 

342 

•65 

*For  the  sake  of  brevity  the  factors  will  be  designated  as  follows : 

1.  Binet-Simon  Tests  3.  Attempts 

2.  Solutions  4.  Time. 

Since  r14.23  =  .06,  factor  4  has  nothing  in  common  with  the 
criterion  that  is  not  contained  in  factors  2  and  3.  In  like  man¬ 
ner,  since  r13.2  =  .03,  factor  3  has  nothing  in  common  with  the 
criterion  that  is  not  contained  in  factor  2.  Nothing  will  be  lost, 
therefore,  as  far  as  the  criterion  is  concerned,  by  discarding 
time  and  attempts  from  the  final  score.  For  the  present  purpose, 
then,  we  shall  use  only  the  number  of  solutions  as  the  final  score. 
The  formula  for  multiple  correlation  shows  that  it  is  not  possible 
by  combining  the  factors  to  get  a  higher  correlation  with  the 
criterion  than  .27.  The  range  of  solutions  is  so  small  that  the 
scores  are  bunched  considerably.  This  probably  affects  the  cor¬ 
relation  somewhat,  but  there  is  no  way  to  remedy  it.  It  cannot 
be  raised  by  using  the  other  factors  in  any  way.  The  present 
method  has  for  its  purpose  to  get  the  highest  correlation  with 
the  criterion. 

(2)  Analysis  of  Data. 

There  is  a  “present  but  low”  positive  correlation  between  the 
criterion  and  time  and  between  the  criterion  and  solutions.  The 
correlation  is  negligible,  however,  between  the  criterion  and  the 
number  of  attempts.  Since  the  variability29  is  the  same  in  each 
kind  of  data,  each  factor  may  be  directly  compared  with  the 
criterion  by  reference  to  Table  XIX.  Thus,  for  every  unit-change 
in  solutions  there  will  be  a  like  change  of  .26  of  a  unit  in  the 
criterion,  and  vice  versa. 

29  The  standard  deviations  for  time,  attempts,  and  solutions  are  16.57,  16.54, 
and  16. 1  respectively. 


INTERRELATION  OF  HIGHER  LEARNING  PROCESSES  37 


The  factors,  solutions  and  time,  have  something  in  common 
with  the  criterion.  Solutions  have  most  and  contain  elements  not 
contained  in  either  of  the  other  factors.  Time  contains  nothing 
with  respect  to  the  criterion  that  is  not  contained  also  in  solutions. 
Each  of  the  factors  is  composed  largely  of  elements  not  found 
in  the  criterion.  Solutions  and  attempts  have  a  high  correlation 
with  each  other  as  have  time  and  attempts.  The  correlation  of 
solutions  and  time  is  marked. 

The  correlation-ratios  for  each  of  the  factors  with  the  criterion 
are  as  follows : 

12  =  .49  and  .54 

13  —  *3°  and  .42 

14  =  .40  and  .44 

These  values  substituted  in  the  Blakeman  formula  give  results 
as  follows : 

Tests  1  and  2,  2.71  and  3.05 

Tests  1  and  3,  1.52  and  2.42 

Tests  1  and  4,  2.21  and  2.50 

According  to  our  test,  the  correlation  of  the  criterion  and 
solutions  is  non-linear.  The  other  two  correlations  are  linear. 
A  table  will  be  constructed  to  show  the  regression  lines  in  the 
correlation  of  solutions  and  the  Binet-Simon  tests.  This  will  be 
postponed,  however,  until  the  final  scores  are  analyzed. 

VIII.  The  Tait  Labyrinth  Puzzle 

(1)  Description  of  Test  and  Method  of  Scoring. 

In  this  test  the  subject  was  given  a  figure  of  the  Tait  Labyrinth 
Puzzle  and  a  copy  of  the  instructions.  Freeman30  has  given  sug¬ 
gestions  as  to  its  use.  Lindley31  also  used  it  in  his  “Study  of 
Puzzles.”  The  figure  and  instructions  are  here  given. 

“You  have  before  you  a  figure  that  can  be  drawn  without  lift¬ 
ing  the  pencil  from  the  paper  and  without  retracing.  Your  pro¬ 
blem  is  to  draw  the  figure  without  lifting  the  pencil  from  the 
paper  and  without  retracing.  As  soon  as  you  are  ready  you  may 
begin  on  this  blank  sheet  of  paper.  You  may  keep  the  figure 

3°  Freeman,  F.  N.,  Experimental  Education ,  IQ1^,  36  ff. 

3i  Lindley,  E.  H.,  Study  of  Puzzles,  Amer.  J.  of  Psychol,  8,  430  ff. 


38 


B.  F.  H AUGHT 


before  you  and  refer  to  it  during  the  drawing  if  you  wish.  No 
attention  will  be  given  to  the  technical  excellence  of  the  drawing. 
If  you  fail  in  the  first  attempt,  take  another  sheet  of  paper  and 
try  it  again.  Continue  until  you  have  made  the  figure  three  times 

Fig.  III.  Showing  the  Tait  Labyrinth  Puzzle. 


in  succession  without  any  errors.  You  are  to  be  judged  by  the 
number  of  trials  required  for  the  learning  and  by  the  number  of 
minutes  used.” 

When  the  subject  started,  the  time  was  noted  and  then  noted 
again  when  the  problem  was  complete.  This  time  included  that 
used  in  reading  the  directions  as  well  as  that  used  in  solving  the 
problem.  It  was  thought  necessary  to  include  the  time  used  in 
reading  the  directions,  since  so  many  will  trace  the  pencil  in  the 
air  over  the  figure  before  trying  to  draw  it  on  paper. 

If  we  designate  the  number  of  trials  by  2  and  the  number  of 
minutes  by  3,  the  correlations  are  as  given  in  Table  XXI. 

The  best  possible  combination  of  time  and  trials  gives  a  cor¬ 
relation  of  .30  with  the  Binet-Simon  tests.  Since  r13.2  gives  a 
correlation  of  .01,  there  is  nothing  common  to  time  and  the 
criterion  that  is  not  contained  in  trials.  Therefore  the  final  scores 
for  comparison  with  the  criterion  will  consist  of  the  percentile 
ranks  in  number  of  trials. 

(2)  Analysis  of  Data. 

There  is  a  “present  but  low”  positive  correlation  between  the 
criterion  and  number  of  trials.  The  correlation  of  the  criterion 

with  the  number  of  minutes,  however,  is  “negligible.”  Since  the 


INTERRELATION  OF  HIGHER  LEARNING  PROCESSES 


39 


Table  XX.  Showing  the  Number  of  Trials,  the  Number  of  minutes,  and 
the  Percentile  Rank  in  Each  Kind  of  Data  in  Tait  Labyrinth  Puzzle. 


Subject 

Score  in 

Per.  Rank  in 

Subject 

Score  in 

Per.  Rank  in 

Trials 

Time 

Trials 

1  Time 

Trials 

Time 

Trials 

Time 

i 

11 

6 

43 

66 

38 

34 

52 

14 

14 

2 

19 

24 

31 

33 

39 

5 

11 

67 

50 

3 

6 

8 

59 

59 

40 

17 

10 

35 

54 

4 

5 

10 

67 

54 

4i 

6 

11 

59 

50 

5 

6 

6 

59 

66 

42 

5 

7 

67 

63 

6 

12 

13 

42 

46 

43 

6 

10 

59 

54 

7 

14 

14 

37 

45 

44 

25 

3i 

23 

21 

8 

22 

21 

27 

38 

45 

7 

12 

57 

48 

9 

5 

6 

67 

66 

46 

10 

11 

46 

50 

10 

25 

24 

23 

33 

47 

9 

7 

50 

63 

n 

5 

22 

67 

37 

48 

17 

29 

35 

25 

12 

9 

10 

50 

54 

49 

9 

18 

50 

21 

13 

3 

13 

82 

46 

50 

14 

26 

37 

28 

14 

7 

7 

57 

63 

5i 

5 

9 

67 

57 

15 

25 

24 

23 

33 

52 

13 

23 

40 

35 

16 

13 

25 

40 

30 

53 

10 

8 

46 

59 

17 

17 

30 

35 

23 

54 

12 

17 

42 

42 

18 

11 

4 

43 

72 

55 

18 

13 

33 

46 

19 

6 

8 

59 

59 

56 

18 

67 

33 

0 

20 

10 

11 

46 

50 

57 

25 

17 

23 

42 

21 

22 

19 

28 

40 

58 

10 

10 

46 

54 

22 

9 

4 

50 

72 

59 

13 

15 

40 

43 

23 

11 

19 

43 

40 

60 

8 

7 

53 

63 

24 

8 

7 

53 

63 

61 

5 

11 

67 

50 

25 

8 

10 

53 

54 

62 

4 

4 

76 

72 

26 

20 

26 

3i 

28 

63 

5 

15 

67 

43 

27 

5 

8 

67 

59 

64 

7 

3 

57 

78 

28 

8 

2 

53 

84 

65 

8 

23 

53 

35 

29 

3 

5 

82 

68 

66 

8 

33 

53 

18 

30 

9 

4 

50 

72 

67 

10 

12 

46 

48 

31 

13 

21 

40 

38 

68 

5 

3 

67 

78 

32 

3 

8 

82 

59 

69 

10 

11 

46 

50 

33 

14 

23 

37 

35 

70 

6 

2 

59 

84 

34 

9 

24 

50 

33 

7i 

38 

14 

0 

45 

35 

5 

10 

67 

54 

72 

4 

10 

76 

54 

36 

6 

9 

59 

57 

73 

5 

4 

67 

72 

37 

13 

8 

40 

59 

74 

8 

19 

53 

40 

Table  XXI.  Showing  the  Correlations  and  Partial  Correlations  of  Each 
Factor  in  the  Tait  Labyrinth  Puzzle  with  the  Binet-Simon  Tests. 


12 

•30 

123 

.26 

13 

•  17 

132 

.01 

23 

•55 

40 


B.  F.  H AUGHT 


variability32  is  the  same  in  each  kind  of  data,  each  factor  may  be 
compared  directly  with  the  criterion  by  reference  to  Table  XXI. 
Thus,  for  every  unit  change  in  number  of  trials  there  will  be  a 
like  change  of  .30  of  a  unit  in  the  criterion  and  vice  versa. 

It  has  already  been  noted  that  time  contains  nothing  with  re¬ 
spect  to  the  criterion  that  is  not  contained  in  number  of  repeti¬ 
tions.  Trials  and  minutes  show  a  “marked”  correlation  with 
each  other. 

The  correlation-ratios  of  the  factors  of  this  test  with  the 
criterion  are : 

12  =  .46  and  .54 

13  =  -33  and  .44 

When  these  values  are  substituted  in  Blakeman’s  formula,  re¬ 
sults  as  follows  are  obtained : 

For  tests  1  and  2,  2.22  and  2.86 

For  tests  1  and  3,  1.80  and  2.59 

One  of  the  regression  lines  in  each  correlation  is  linear  and  the 
other  non-linear.  Table  XXII  shows  the  correspondence  be¬ 
tween  time  and  the  criterion.  The  regression  line  of  the  means 
of  the  columns  is  relatively  linear  and  shows  an  increase  in 
y-values  with  an  increase  in  x-values  from  the  lowest  to  the  high¬ 
est  percentile.  The  regression  line  of  the  means  of  the  rows  is 
relatively  non-linear.  It  shows  a  rapid  increase  in  x-values  with 
an  increase  in  y-values  from  the  twentieth  to  the  fortieth  per¬ 
centile.  The  x-values  change  very  little  until  the  sixtieth  per¬ 
centile  is  reached  and  then  the  increase  is  again  rapid. 

Since  the  percentile  ranks  in  trials  are  used  as  the  final  scores, 
the  table  showing  the  correspondence  between  this  factor  and 
the  criterion  will  be  postponed  until  the  next  section. 

IX.  Intercorrelations 

(i)Tests  Analyzed  in  the  Light  of  the  Criterion. 

We  shall  first  analyze  the  scores  in  the  light  of  the  criterion. 
The  final  scores  are  obtained  in  Rational  Learning  by  combining 
repetitions  and  perseverative  errors  equally,  in  Rational  Learn- 

32  The  standard  deviations  for  trials  and  time  are  16.33  and  16.58  re¬ 
spectively. 


INTERRELATION  OF  HIGHER  LEARNING  PROCESSES 


4i 


Table  XXII.  Showing  the  Distribution  of  Subjects  on  the  Basis  of  Time  in 
the  Tait  Labyrinth  Puzzle  and  the  Binet-Simon  Tests.  Circles  through 
which  the  broken  line  passes  represent  the  means  of  the  columns 
and  those  through  which  the  continuous  line  passes  represent  the 
means  of  the  rows.  Each  asterisk  represents  a  subject. 


Table  XXIII.  Showing  the  Correlations  and  Partial  Correlations  for  the 
Final  Scores*  with  the  Binet-Simon  Tests.* 


12 

•33 

13 

•47 

14 

.26 

15 

.30 

12-3 

.20 

13-2 

.40 

14-2 

•  17 

152 

.19 

12-4 

.27 

13-4 

43 

14-3 

•  13 

15-3 

.25 

12-5 

.24 

13-5 

•45 

14-5 

.19 

15-4 

•25 

12-34 

.18 

13-24 

.38 

14-23 

.09 

15-23 

.19 

12-35 

.11 

13-25 

.40 

14-25 

•  14 

15-24 

•  17 

12-45 

.21 

13-45 

42 

14-35 

.07 

15-34 

.22 

12-345 

.11 

13-245 

.38 

14-235 

.06 

15-234 

.18 

♦The  numbers  have  the  following  meaning: 

1.  Binet-Simon  Tests. 

2.  Rational  Learning. 

3.  Rational  Learning  (Modified). 

4.  Checker  Puzzle. 

5.  Tait  Labyrinth  Puzzle. 


42 


B.  F.  H AUGHT 


ing  (Modified)  by  combining  minutes  and  unclassified  errors 
equally,  in  the  Checker  Puzzle  by  taking  the  solutions,  and  in 
the  Tait  Labyrinth  Puzzle  by  taking  the  number  of  trials. 

(a)  Rational  Learning.  There  is  a  “present  but  low”  positive 
correlation  between  the  final  scores  in  Rational  Learning  and  the 
criterion.  The  correlation  is  partly  due  to  elements  found  also 
in  Rational  Learning  (Modified),  found  to  a  less  extent  in  the 
Tait  Labyrinth  Puzzle,  and  to  a  still  less  extent  in  the  Checker 
Puzzle.  The  correlation  is  significant  when  the  common  ele¬ 
ments  in  any  one  of  the  other  three  tests  are  removed,  but  when 
the  common  elements  found  also  in  all  the  other  three  tests  are 
removed,  the  correlation  is  no  longer  significant.  In  other  words, 
everything  common  to  the  criterion  and  Rational  Learning  is 
found  in  the  other  three  tests. 

The  correlation  ratios  for  The  Binet-Simon  tests  and  Rational 
Learning  are  .47  and  .51.  These  values  substituted  in  Blake- 
man’s  formula  give  2.13  and  2.47,  which  indicate  that  for  all 
practical  purposes  the  correlation  is  linear. 

Rational  Learning  seems  to  measure  some  mental  functions 
not  detected  by  the  Binet-Simon  tests.  The  first  that  may  be 
mentioned  is  that  of  being  able  to  attack  and  solve  a  problem 
without  getting  confused.  In  support  of  this  statement  some 
special  cases  are  cited.  Subject  6  scores  “high”  in  each  factor 
of  Rational  Learning,  but  “low”  in  the  criterion.  She  grasped 
the  situation  quickly  and  completed  the  learning  with  only  23 
errors.  Subject  9  scores  “high”  in  unclassified,  logical,  and  per- 
severative  errors,  but  “low”  in  the  criterion.  She  made  only  17 
errors  in  the  first  repetition  and  finished  with  a  total  of  21.  We 
have  altogether  nine  subjects  who  score  “low”  in  the  criterion 
and  “high”  in  one  or  more  factors  in  Rational  Learning.  An 
examination  of  the  individual  records  shows  that  in  every  case 
the  learning  was  completed  without  confusion  or  distraction. 

A  second  mental  function  that  Rational  Learning  seems  to 
test  better  than  does  the  criterion  is  the  ability  to  give  attention 
longer  and  to  more  elements  than  is  usually  required  in  the  latter 
tests.  Subject  26  illustrates  this  point  fairly  well.  She  scores 


INTERRELATION  OF  HIGHER  LEARNING  PROCESSES 


43 


“high’  in  the  criterion  and  “low"  in  repetitions  and  perseverative 
errors.  She  has  88  unclassified  errors  altogether  and  70  of  these 
were  made  in  the  first  two  repetitions.  The  other  18  are  distrib¬ 
uted  from  the  third  to  the  eighth  inclusive.  The  record  indicates 
that  the  learning  was  almost  complete  in  the  third  repetition,  in 
which  only  two  errors  were  made,  yet  five  more  repetitions  were 
required.  Subjects  34  and  42  have  records  similar  to  that  of  26; 
that  is,  they  have  a  few  errors  distributed  over  several  repetitions, 
a  condition  which  indicates  a  lack  of  attention. 

A  third  mental  function  or  process  measured  better  by  Rational 
Learning  than  by  the  criterion  is  the  kind  of  attack.  Some  sub¬ 
jects  read  the  instructions  and  make  sure  that  every  point  is  un¬ 
derstood  before  beginning.  Others  read  them  in  a  careless  way 
and  jump  into  the  problem  without  knowing  just  what  is  to  be 
done.  Subject  2  illustrates  the  later  method.  She  made  77  un¬ 
classified  and  44  logical  errors  in  the  first  two  repetitions.  Sub¬ 
ject  72  made  5  of  her  8  perseverative  errors  in  the  first  repetition. 
This  indicates  that  the  instructions  were  not  fully  understood. 

The  fourth  and  last  mental  function  that  seems  to  be  especially 
well  brought  out  by  Rational  Learning  is  the  speed  of  the  subject. 
This  may  be  illustrated  by  subject  72.  She  scores  “high”  in  the 
criterion  and  “low”  in  time  and  perseverative  errors.  She  is  a 
mature  woman  who  goes  at  everything  slowly  and  deliberately. 
Subject  40  also  is  a  good  example.  She  worked  very  slowly  and 
deliberately,  thus  making  a  “high”  score  in  repetitions. 

(b)  Rational  Learning  (Modified).  The  correlation  of  Ra¬ 
tional  Learning  (Modified)  and  the  criterion  is  “marked.’"  The 
elements  common  to  the  two  tests  are  found  to  a  slight  extent 
in  each  of  the  other  three  tests.  The  correlation  of  the  third 
order  shows  that  Rational  Learning  (Modified)  has  elements 
common  to  the  criterion  not  found  in  any  one  of  the  other  three 
tests  or  in  all  of  them  combined.  This  means  that  Rational 
Learning  (Modified)  contains  elements  not  found  in  the  other 
tests. 

The  correlation -ratios  for  Rational  Learning  (Modified)  and 
the  criterion  are  .60  and  .63.  These  values  substituted  in  the 


44 


B.  F.  H AUGHT 


Blakeman  formula  give  2.37  and  2.69,  indicating  that  one  re¬ 
gression  line  is  linear  and  the  other  non-linear.  Table  XXIV 
shows  the  actual  regression  lines.  The  line  joining  the  means 
of  the  rows  is  relatively  linear  and  the  line  joining  the  means  of 
the  columns  is  relatively  non-linear.  The  non-linearity  would 
be  eliminated  if  the  average  of  the  seven  cases  in  the  fifth  column 
from  the  left  were  50  instead  of  26.  The  number  of  cases  in 
each  row  and  column  is  too  small  for  the  non-linearity  to  have 
any  significance  when  the  curve  does  not  take  any  well  defined 
shape. 


Table  XXIV.  Showing  the  Distribution  of  Subjects  on  the  Basis  of  Ra¬ 
tional  learning  (Modified)  and  the  Binet-Simon  Tests.  Circles 
through  which  the  broken  line  passes  represent  the  means  of  the 
columns  and  those  through  which  the  continuous  line  passes  represent 
the  means  of  the  rows.  Each  asterisk  represents  a  subject. 


Rational  Learning  (Modified) 


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In  Rational  Learning,  repetitions  and  perseverative  errors  are 
the  significant  factors.  In  Rational  Learning  (Modified),  how¬ 
ever,  the  significant  factors  are  time  and  unclassified  errors. 
The  cause  of  this  difference  is  interesting  and  can  be  stated  only 


INTERRELATION  OF  HIGHER  LEARNING  PROCESSES  45 


on  a  priori  grounds.  In  the  former,  repetitions  are  more  sig¬ 
nificant  than  time  and  contain  everything  in  time  with  respect 
to  the  criterion.  The  reverse,  however,  is  the  case  with  Ra¬ 
tional  Learning  (Modified).  Time  includes  all  that  is  in  re¬ 
petitions.  The  writer  is  of  the  opinion  that  the  experimenter, 
in  calling  out  the  numbers,  controls  the  speed  of  the  subject  to 
some  extent.  He  enters  into  the  situation  in  a  different  way  from 
what  he  does  when  he  stands  back  and  records  the  responses. 
The  writer  has  found  that  when  a  subject  is  naming  words,  the 
speed  is  checked  if  the  words  are  recorded  in  plain  view  of  the 
subject. 

The  next  problem  is  to  try  to  answer  why  perseverative  errors 
in  Rational  Learning  and  unclassified  errors  in  Rational  Learn¬ 
ing  (Modified)  are  the  significant  factor.  This  also  can  be 
stated  only  on  a  priori  grounds.  It  is  probable  that  in  the  latter 
experiment  space  perception  makes  it  easier  to  avoid  persevera¬ 
tive  errors  than  in  the  former.  The  tendency  seems  to  be  to  go 
from  one  end  of  a  row  to  the  other  and  to  skip  about  here  and 
there  less  than  in  Rational  Learning. 

An  analysis  of  individual  cases  indicates  that  Rational  Learn¬ 
ing  (Modified)  tests  the  same  factors  as  Rational  Learning. 
First,  it  tests  the  subject’s  ability  to  work  for  a  period  of  time 
without  confusion  or  distraction  better  than  the  criterion  does. 
In  support  of  this  some  special  cases  are  cited.  Subject  6  scores 
“low”  in  the  criterion  and  “high”  in  time,  repetitions,  and  un¬ 
classified  errors.  The  data  shows  that  she  was  able  to  con¬ 
centrate  her  attention  and  learn  the  problem  without  confusion. 
Subject  22  scores  “low”  in  the  criterion  and  “high”  in  time, 
repetitions,  and  perseverative  errors.  She  learned  this  test 
quickly  and  was  able  to  avoid  confusion  and  distraction. 

Second,  Rational  Learning  (Modified)  tests  a  subject’s  ability 
to  give  attention  longer  and  to  a  more  complex  situation  than 
that  usually  required  by  the  criterion.  Subject  11  illustrates 
this  point.  She  scores  “high”  in  the  criterion  and  “low”  in 
repetitions.  In  five  of  the  repetitions  only  one  error  was  made 
for  each.  Certainly  close  attention  would  have  cut  down  the  num- 


B.  F.  H AUGHT 


ber.  Subject  49  has.  a  “high”  score  in  the  criterion  and  a  “low” 
one  in  repetitions  and  perseverative  errors.  The  “low”  score 
in  repetitions  of  this  subject  also  is  caused  by  a  lack  of  attention, 
as  was  that  of  subject  11.  This  conclusion  is  based  on  the  fact 
that  she  made  from  zero  to  three  errors  in  each  repetition  from 
the  sixth  to  the  thirteenth.  Subject  61  scored  “high”  in  the 
criterion  and  “low”  in  repetitions  and  perseverative  errors.  She 
made  only  one  error  in  the  third  repetition,  yet  she  required 
thirteen  repetitions  to  complete  the  learning.  The  greatest  num¬ 
ber  of  errors  made  in  any  repetition  after  the  second  is  three. 
This  too  probably  shows  a  lack  of  attention  to  the  correct 
numbers. 

In  the  third  place,  Rational  Learning  (Modified)  is  better  for 
detecting  the  kind  of  attack  than  is  the  criterion.  It  is  possible 
to  determine  whether  the  subject  approaches  the  problem  with 
that  deliberate  method  which  indicates  that  he  is  sure  of  what 
is  to  be  done,  or  approaches  it  in  that  method  characteristic  of 
the  person  who  gets  an  inkling  of  what  is  to  be  done  and  then 
begins  in  a  kind  of  hit-and-miss  sort  of  way. 

The  fourth  mental  function  that  is  revealed  in  this  test  is  the 
speed  of  the  subject.  Here  we  have  reference  to  the  procedure 
after  the  instructions  have  been  read  and  the  subject  has  begun. 
This  is  illustrated  by  subject  66.  He  scores  “high”  in  the 
criterion  and  “low”  in  time.  The  ‘low”  score  in  the  latter  is 
clearly  due  to  the  slow,  deliberate  method  of  work.  Subject  72 
also  scores  “high”  in  the  criterion  and  low  in  time.  Her  scores 
are  almost  identical  with  those  of  subject  66.  She  is  a  mature 
woman  who  worked  very  slowly  and  deliberately. 

(c)  Checker  Puzzle.  There  is  a  “present  but  low”  positive 
correlation  between  the  scores  in  the  Checker  Puzzle  and  the 
criterion.  The  correlation  is  partly  explained  by  elements  found 
also  in  each  of  the  other  tests.  This  test  as  far  as  the  criterion 
is  concerned  is  most  like  Rational  Learning  (Modified  and  least 
like  the  Tait  Labyrinth  Puzzle.  The  correlation  is  not  significant 
when  the  common  elements  found  also  in  the  other  tests  are  re¬ 
moved. 


INTERRELATION  OF  HIGHER  LEARNING  PROCESSES  47 

The  correlation-ratios  for  the  criterion  and  the  Checker  Puz¬ 
zle  are  .49  and  .54.  These  values  substituted  in  Blakeman’s 
formula  give  2.71  and  3.05,  indicating  that  both  of  the  regression 
lines  are  non-linear.  Table  XXV  shows  the  two  regression  lines. 
If  they  were  smoothed  they  would  be  nearly  straight  and  show 
very  little  correlation.  In  other  words  the  high  correlation-ratio 
is  to  a  great  extent  due  to  the  fluctuation  of  the  means  of  the 
rows  and  the  means  of  the  columns. 


Table  XXV.  Showing  the  Distribution  of  Subjects  on  the  Basis  of  the 
Checker  Puzzle  and  the  Binet-Simon  Tests.  Circles  through  which 
the  broken  line  passes  represent  the  means  of  the  columns  and 
those  through  which  the  continuous  line  passes  represent  the  means 
of  the  rows.  Each  asterisk  represents  a  subject. 


Checker  Puxz/e  Test 


Analysis  of  the  individual  cases  shows  no  mental  functions  tested 
by  the  Checker  Puzzle  that  are  not  also  tested  by  the  criterion. 
This  may  be  due  to  the  fact  that  the  responses  of  the  subjects 
cannot  be  recorded  so  exactly  as  in  the  other  tests.  Partial  cor¬ 
relations  of  the  third  order  show  that  this  test  contains  nothing 


48 


B.  F.  H AUGHT 


with  respect  to  the  criterion  that  is  not  contained  in  the  two 
Rational  Learning  Tests. 

(d)  Tait  Labyrinth  Puzzle.  The  correlation  between  the 
criterion  and  the  Tait  Labyrinth  Puzzle  is  positive  and  “present 
but  low.”  The  correlation  is  partly  due  to  elements  found  also 
in  Rational  Learning,  and  to  a  less  extent  to  elements  found  in 
Rational  Learning  (Modified)  and  the  Checker  Puzzle.  The 
correlation  is  barely  significant  when  the  elements  common  to 
all  three  tests  are  removed. 

The  individual  cases  reveal  no  mental  functions  tested  by  the 
Tait  Labyrinth  Puzzle  that  are  not  tested  by  the  criterion. 

The  correlation-ratios  for  the  criterion  and  the  Tait  Labyrinth 
Puzzle  are  .46  and  .54.  These  values  substituted  in  the  Blake- 
man  formula  give  2.22  and  2.86,  indicating  that  one  regression 

Table  XXVI.  Showing  the  Distribution  of  Subjects  on  the  Basis  of  the 
Tait  Labyrinth  Puzzle  and  the  Binet-Simon  Test.  Circles  through 
which  the  broken  line  passes  represent  the  means  of  the  columns  and 
those  through  which  the  continuous  line  passes  represent  the  means  of 
the  rows. 


INTERRELATION  OF  HIGHER  LEARNING  PROCESSES  49 


line  is  linear  and  the  other  non-linear.  The  line  joining  the 
means  of  the  rows  is  linear  and  the  other  is  non-linear.  Table 
XXVI  shows  the  two  regression  lines. 

*(2)  Interrelation  of  Tests  Scored  in  the  Light  of  the  Criterion. 

The  four  tests  are  here  compared  with  each  other  as  they  are 
scored  in  the  light  of  the  criterion. 

Table  XXVII.  Showing  the  Correlations  and  Partial  Correlations  of  the 
Four  Tests,  When  Scored  in  the  Light  of  the  Criterion.* 


23 

.36 

24 

.32 

25 

.41 

23-4 

.29 

24-3 

.23 

25-3 

.38 

23-5 

.32 

24-5 

.24 

25-4 

.36 

23  45 

.27 

24-35 

.17 

25-34 

•35 

34 

.32 

35 

.18 

45 

.26 

34-2 

.23 

35-2 

.04 

45-2 

U5 

34-5 

.28 

35-4 

.11 

45-3 

.22 

34-25 

.22 

35-24 

.01 

45-23 

.14 

*  The  numbers  have  the  same  meanings  as  in  Table  XXIII. 

Rational  Learning  has  a  “present  but  low”  positive  correlation 
with  Rational  Learning  (Modified)  and  with  the  Checker  Puzzle. 
It  has  a  “marked”  correlation  with  the  Tait  Labyrinth  Puzzle. 
There  are  elements  common  to  Rational  Learning  and  Rational 
Learning  (Modified)  that  are  not  found  in  the  Checker  Puzzle 
and  the  Tait  Labyrinth  Puzzle.  In  like  manner  there  are  elements 
common  to  Rational  Learning  and  the  Tait  Labyrinth  Puzzle 
that  are  not  found  in  the  other  two  tests.  The  correlation  of 
Rational  Learning  with  the  other  three  tests  combined  is  .53. 

The  correlation  of  Rational  Learning  (Modified)  and  the 
Checker  Puzzle  is  “present  but  low.”  The  correlation  with  the 
Tait  Labyrinth  Puzzle  is  barely  significant.  There  are  elements 
common  to  Rational  Learning  (Modified)  and  the  Checker 
Puzzle  not  found  in  the  other  two  tests.  The  correlation  of  this 
test  with  the  other  three  combined  is  .48. 

The  Checker  Puzzle  has  a  “present  but  low”  positive  correla¬ 
tion  with  the  Tait  Labyrinth  Puzzle.  The  correlation  is  mostly 
due  to  elements  found  also  in  Rational  Learning  and  Rational 
Learning  (Modified).  The  correlation  with  the  other  three 
tests  combined  is  .41. 

The  Tait  Labyrinth  Puzzle  has  a  correlation  with  the  other 


50 


B.  F.  H AUGHT 


Table  XXVIII.  Showing  the  Distribution  of  Subjects  on  the  Basis  of  Ra¬ 
tional  Learning  and  Rational  Learning  (Modified).  Circles  through 
which  the  broken  line  passes  represent  the  means  of  the  columns  and 
those  through  which  the  continuous  line  passes  represent  the  means 
of  the  rows.  Each  asterisk  represents  a  subject. 


x*  Rational  L  earning  (Modified) 


three  tests  combined  of  .43.  The  multiple  correlations  may  be 
summarized  as  follows: 

^•2(345)  ~  *53 

-^•3(245)  ~  48 

R4G35)  =  -41 
■^5(234)  =  -43 

After  allowance  is  made  for  errors  and  non-linearity,  it  seems  safe 
to  conclude  that  each  of  these  tests  contains  elements  that  are  not 
found  in  any  of  the  others.  The  correlation-ratios  for  the  inter¬ 
relations  are  as  follows : 


INTERRELATION  OF  HIGHER  LEARNING  PROCESSES 


5i 


23  —  .51  and  .57 

24  =  .46  and  .60 

25  =  47  and  .51 

34  =  .51  and  .58 

35  =  -35  and  .51 
45  =  43  and  .46 

When  these  values  are  substituted  in  the  Blakeman  formula,  re¬ 
sults  obtained  are  as  follows : 


Tests  2  and  3, 
Tests  2  and  4, 
Tests  2  and  5, 
Tests  3  and  4, 
Tests  3  and  5, 
Tests  4  and  5, 


2.30  and  2.82 
2.02  and  3.23 
1.46  and  1.93 
2.01  and  3.08 
1 .9 1  and  3.04 
2.18  and  2.42 


Table  XXIX.  Showing  the  Distribution  of  Subjects  on  the  Basis  of  Ra¬ 
tional  Learning  and  the  Checker  Puzzle.  Circles  through  which  the 
broken  line  passes  represent  the  means  of  the  columns  and  those 
through  which  the  continuous  line  passes  represent  the  means  of  the 
rows.  Each  asterisk  represents  a  subject. 


*a  Checker  Puzzle  Test 


52 


B.  F.  H AUGHT 


Four  of  the  six  correlations  are  non-linear  according  to  the  Blake- 
man  test.  The  correlation  of  tests  2  and  5  and  of  tests  4  and  5 
may  be  considered  linear.  Tables  showing  the  lines  of  the  means 
of  the  columns  and  the  means  of  the  rows  will  now  be  con¬ 
structed  for  the  non-linear  correlations. 

Table  XXVIII  shows  the  correspondence  between  the  scores 
in  Rational  Learning  and  Rational  Learning  (Modified).  The 
lines  appear  linear  from  the  thirteenth  to  the  sixteenth  percentiles 

Table  XXX.  Showing  the  Distribution  of  Subjects  on  the  Basis  of  Ra¬ 
tional  Learning  (Modified)  and  the  Checker  Puzzle.  Circles  through 
which  the  broken  line  passes  represent  the  means  of  the  columns 
and  those  through  which  the  continuous  line  passes  represent  the 
means  of  the  rows.  Each  asterisk  represents  a  subject. 


x*  Checker  Puzzle  Test 


and  show  a  high  correlation  within  these  limits.  Outside  of 
these  limits,  however,  the  fluctuations  are  marked  and  conse¬ 
quently  the  correlation-ratio  becomes  larger  than  the  correlation. 

Table  XXIX  shows  the  correspondence  between  the  scores  in 
Rational  Learning  and  Checker  Puzzle.  These  regression  lines 
when  smoothed  will  be  approximately  straight  and  will  show  a 


INTERRELATION  OF  HIGHER  LEARNING  PROCESSES 


53 


Table  XXXI.  Showing  the  Distribution  of  Subjects  on  the  Basis  of  Ra¬ 
tional  Learning  (Modified)  and  the  Tait  Labyrinth  Puzzle.  Circles 
through  which  the  broken  line  passes  represent  the  means  of  the 
columns  and  those  through  which  the  continuous  line  passes  represent 
the  means  of  the  rows.  Each  asterisk  represents  a  subject. 


x *  Toil  Labyrinth  'Puzzle 


low  positive  correlation.  An  increase  in  ability  to  do  the  Checker 
Puzzle  shows  an  increase  in  ability  to  do  Rational  Learning. 
The  reverse,  however,  is  not  so  true.  An  increase  in  ability  to 
perform  Rational  Learning  does  not  show  very  much  change  in 
ability  to  perform  the  Checker  Puzzle. 

Table  XXX  shows  the  correspondence  between  the  scores  in 
Rational  Learning  (Modified)  and  the  Checker  Puzzle.  The 
line  of  the  means  of  the  rows  smoothed  will  be  approximately 
straight,  but  the  other  regression  line  will  be  far  from  straight. 
There  seems  to  be  closer  agreement  between  the  two  sets  of 
scores  in  the  upper  quartiles  than  in  the  lower. 

Table  XXXI  shows  the  agreement  of  scores  in  Rational  Learn¬ 
ing  (Modified)  and  the  Tait  Labyrinth  Puzzle.  An  increase  in 
ability  in  Rational  Learning  (Modified)  is  accompanied  by  an 


54 


B.  F.  H AUGHT 


increase  in  ability  in  the  Tait  Labyrinth  Puzzle.  Here  again, 
the  reverse  is  not  true.  After  the  fiftieth  percentile,  an  increase 
in  ability  in  the  Tait  Labyrinth  Puzzle  is  accompanied  by  a  de¬ 
crease  in  ability  in  Rational  Learning  (Modified). 

(3)  Interrelation  of  Tests  Scored  by  Combining  the  Factors 
Equally. 

The  next  step  will  be  to  analyze  the  four  tests  when  scored 
by  combining  all  the  factors  equally.  The  final  scores  in  Rational 
Learning  are  obtained  by  adding  together  the  percentile  ranks 
in  time,  repetitions,  unclassified,  logical  and  perseverative  errors 
and  then  reducing  to  absolute  percentiles  by  use  of  Rugg’s  table. 
The  final  scores  in  the  other  tests  are  found  in  a  similar  manner. 

Table  XXXII.  Showing  the  Correlations  and  Partial  Correlations, 
When  Scored  by  Combining  All  the  Factors  Equally.* 


23 

•33 

24 

.18 

25 

.44 

23-4 

.29 

24*3 

.06 

25-3 

•37 

23*5 

.21 

24-5 

.08 

25-4 

.41 

23-45 

.20 

24-35 

.01 

25-34 

•37 

34 

.38 

35 

•33 

45 

.26 

34*2 

•34 

35-2 

.21 

45-2 

.20 

34-5 

•32 

35-4 

.26 

45-3 

•15 

34-25 

•31 

35-24 

•15 

45-23 

.14 

*  The  numbers  have  the  same  meaning  as  in  Table  XXIII. 

Rational  Learning  has  something  in  common  with  each  of 
the  other  tests.  It  is  most  like  the  Tait  Labyrinth  Puzzle  and 
least  like  the  Checker  Puzzle.  The  correlation  with  the  former 
is  “marked”  and  with  the  latter  is  barely  significant.  Every¬ 
thing  in  the  Checker  Puzzle  common  to  Rational  Learning  is 
also  found  in  the  Tait  Labyrinth  Puzzle,  and  in  Rational  Learn¬ 
ing  (Modified).  There  are  elements  common  to  Rational  Learn¬ 
ing  and  Rational  Learning  (Modified)  that  are  not  found  in 
the  Checker  Puzzle  and  the  Tait  Labyrinth  Puzzle.  In  like 
manner  there  are  elements  common  to  Rational  Learning  and 
the  Tait  Labyrinth  Puzzle  that  are  not  found  in  the  other  two 
tests.  The  correlation  of  Rational  Learning  with  the  other  three 
tests  is  .48. 

Rational  Learning  (Modified)  has  a  “present  but  low”  positive 
correlation  with  the  Checker  Puzzle  and  with  the  Tait  Laby- 


INTERRELATION  OF  HIGHER  LEARNING  PROCESSES 


55 


rinth  Puzzle.  The  correlation  with  the  other  three  tests  com¬ 
bined  is  .48.  This  means  that  there  is  much  in  this  test  common 
to  the  other  three  tests  and  much  that  is  not  found  in  them. 

The  Checker  Puzzle  test  has  a  low  correlation  with  the  Tait 
Labyrinth  Puzzle.  It  correlates  with  the  other  three  tests  com¬ 
bined  to  the  extent  of  .40.  The  Tait  Labyrinth  Puzzle  has  a 
correlation  with  the  three  remaining  tests  of  .49.  The  multiple 
correlations  may  be  summarized  as  follows : 

■^•2(345)  =:::  *4-8 

R3G45)  =  *4& 

^-4(235)  -4° 

■^5(234)  ~  -49 


We  may  safely  conclude  that  each  of  these  tests  contains  much 
that  is  not  found  in  any  of  the  other  tests.  The  correlation-ratios 
are  as  follows: 

23  =  -45  and  -49 

24  =  .33  and  .54 

25  =  .50  and  .61 

34  =  -53  and  -59 

35  —  -47  and  .49 

45  =  .40  and  .47 


When  these  values  are  substituted  in  Blakeman’s  formula,  the 
following  results  are  obtained : 


For  tests  2  and  3, 
For  tests  2  and  4, 
For  tests  2  and  5, 
For  tests  3  and  4, 
For  tests  3  and  5, 
For  tests  4  and  5, 


1.95  and  2.30 
1.76  and  3.24 
1. 51  and  2.61 
2.35  and  2.88 
2.13  and  2.30 

1.96  and  2.49 


According  to  the  Blakeman  test  three  of  the  correlations  are 
linear  and  three  are  non-linear.  The  correlation  of  Rational 
Learning  with  Rational  Learning  (Modified)  is  linear,  but  with 
the  Checker  Puzzle  and  the  Tait  Labyrinth  Puzzle  it  is  non¬ 
linear.  The  correlation  of  Rational  Learning  (Modified)  with 
the  Checker  Puzzle  is  non-linear,  but  with  the  Tait  Labyrinth 


56 


B.  F.  H AUGHT 


Puzzle  it  is  linear.  The  correlation  of  the  Checker  Puzzle  with 
the  Tait  Labyrinth  Puzzle  is  linear. 

Table  XXXIII  shows  the  correspondence  between  scores  in  Ra¬ 
tional  Learning  and  the  Checker  Puzzle.  The  line  joining  the 
means  of  the  rows  shows  that  as  ability  in  Rational  Learning 

Table  XXXIII.  Showing  Distribution  of  Subjects  on  the  Basis  of  Ra¬ 
tional  Learning  and  the  Checker  Puzzle.  Circles  through  which  the 
broken  line  passes  represent  the  means  of  the  columns  and  those 
through  which  the  continuous  line  passes  represent  the  means  of  the 
rows.  Each  asterisk  represents  a  subject. 


increases  there  is  not  much  change  in  ability  in  the  Checker 
Puzzle  until  the  seventieth  percentile  is  reached  and  then  the 
increase  is  rapid.  A  smoothed  curve  through  the  means  of  the 
columns  will  show  that  as  ability  in  the  Checker  Puzzle  in¬ 
creases  the  ability  in  Rational  Learning  slowly  increases  until 
the  fifty-fifth  percentile  is  reached  and  then  there  is  a  decrease 
in  ability  up  to  the  seventy-fifth  percentile. 

Table  XXXIV  shows  that  the  agreement  between  the  scores 
in  Rational  Learning  and  the  Tait  Labyrinth  Puzzle  is  not  very 


INTERRELATION  OF  HIGHER  LEARNING  PROCESSES 


57 


Table  XXXIV.  Showing  the  Distribution  of  Subjects  on  the  Basis  of  Ra¬ 
tional  Learning  and  the  Tait  Labyrinth  Puzzle.  Circles  through 
which  the  broken  line  passes  represent  the  means  of  the  columns  and 
those  through  which  the  continuous  line  passes  represent  the  means 
of  the  rows.  Each  asterisk  represents  a  subject. 


close.  A  smoothed  curve  through  the  means  of  the  rows  in¬ 
dicates  that  as  ability  in  Rational  Learning  increases,  there  is  a 
slight  increase  in  ability  to  solve  the  Tait  Labyrinth  Puzzle  up 
to  the  sixty-fifth  percentile  and  then  a  slight  decrease  in  ability 
from  this  point  on.  The  line  joining  the  means  of  the  columns 
is  very  irregular.  Beginning  with  the  twenty-fifth  percentile, 
as  ability  to  solve  the  Tait  Labyrinth  Puzzle  increases,  there  is 
a  rapid  increase  in  ability  in  Rational  Learning.  From  this  point 
on,  there  is  little  relation  between  the  two  sets  of  abilities. 

Table  XXXV  shows  the  agreement  between  the  scores  in 
Rational  Learning  (Modified)  and  the  Checker  Puzzle.  The 
line  joining  the  means  of  the  columns  is  linear  according  to  the 
Blakeman  test.  It  shows  that  as  ability  to  solve  the  Checker 
Puzzle  increases,  there  is  also  a  constant  but  slow  increase  in 


58  B.  F.  H AUGHT 

Table  XXXV.  Showing  the  Distribution  of  Subjects  on  the  Basis  of  Ra¬ 
tional  Learning  (Modified)  and  the  Checker  Puzzle.  Circles  through 
which  the  broken  line  passes  represent  the  means  of  the  columns 
and  those  through  which  the  continuous  line  passes  represent  the 
means  of  the  rows.  Each  asterisk  represents  a  subject. 


x-Che chet'  Puzzle  Test 


ability  in  Rational  Learning  (  Modified).  The  line  joining 
the  means  of  the  rows  is  non-linear.  From  the  twentieth  to 
the  thirtieth  percentiles,  ability  in  the  Checker  Puzzle  decreases 
with  an  increase  in  ability  in  Rational  Learning  (Modified). 
From  the  thirtieth  percentile  on,  there  is  a  slight  increase  in 
ability  to  solve  the  Checker  Puzzle  as  the  ability  in  Rational 
Learning  (Modified)  increases. 

X.  A  Discussion  of  Learning  and  Intelligence 

Learning  of  the  reflective  or  problem  solving  kind  has  often 
been  looked  upon  as  involving,  among  other  factors,  one  general 
mental  function  or  process.  It  has  been  assumed  that  the  per¬ 
son  who  has  good  reasoning  ability  in  one  problem  will  be  good 
in  all  others  of  this  same  general  type.  This  conception  implies 


INTERRELATION  OF  HIGHER  LEARNING  PROCESSES 


59 


that  there  is  always  a  high  correlation  between  any  two  such 
problems.  In  this  investigation,  however,  the  correlations  are 
not  high.  In  fact,  they  are  all  comparatively  low.  The  lowest 
is  .18  and  the  highest  .44.  The  conclusion  is  that  there  is  not 
one  general  rational  learning  process,  but  a  number  of  processes. 
Two  tests  as  similar  as  Rational  Learning  and  Rational  Learning 
(Modified),  although  they  have  something  in  common,  are  to  a 
large  degree  independent  of  each  other,  since  they  have  a  cor¬ 
relation  of  only  .36.  This  conception  that  any  two  tests  have 
something  in  common  and  something  that  is  not  common  has 
been  explained  in  two  ways.  The  first  is  the  Two  Factor  theory 
of  intelligence  set  forth  by  Spearman.  The  second  assumes  that 
each  activity,  such  as  a  mental  test  or  learning  problem,  involves 
a  specific  number  of  factors  combined  in  a  specific  way.  These 
two  theories  will  now  be  treated  in  order. 

Spearman  set  forth  his  Two  Factor  theory  of  intelligence  in 
1904.  His  first  statement  of  the  theory  was  as  follows:  “All 
branches  of  intellectual  activity  have  in  common  one  funda¬ 
mental  function  (or  group  of  functions),  whereas  the  remain¬ 
ing  or  specific  elements  of  the  activity  seem  in  every  case  to  be 
wholly  different  from  that  in  all  the  others.”33  This  statement 
should  be  supplemented  by  the  following  explanation : 

“It  was  never  asserted,  then,  that  the  general  factor  prevails 
exclusively  in  the  case  of  performances  too  alike :  it  was  only 
said  that  when  this  likeness  is  diminished  (or  when  the  resem¬ 
bling  performances  are  pooled  together),  a  point  is  soon  reached 
where  the  correlations  are  still  of  a  considerable  magnitude,  but 
now  indicate  no  common  factor  except  the  General  one.  The 
latter,  it  was  urged,  produces  the  basal  correlation,  while  the 
similarities  merely  superpose  something  more  or  less  adventi¬ 
tious.”34 

His  most  recent  statement  of  the  theory  is: 

“The  purport  of  this  theory  is  that  the  cognitive  performances 

33  Spearman,  C.,  General  Intelligence,  Objectively  Determined  and  Meas¬ 
ured,  Amer.  J.  Psychol.,  1904,  15,  201  ff. 

34  Hart,  B.,  and  Spearman,  C.,  General  Ability,  Its  Existence  and  Nature, 
Brit.  J.  of  Psychol,  1912,  5,  51  ff. 


Co 


B.  F.  H AUGHT 


of  any  person  depend  upon  :  (a)  A  general  factor  entering  more 
or  less  into  them  all;  and  (b)  a  specific  factor  not  entering  ap¬ 
preciably  into  any  two,  so  long  as  these  have  a  certain  quite 
moderate  degree  of  unlikeness  to  one  another.”55 

Spearman's  method  was  to  measure  a  number  of  mental 
abilities  in  a  number  of  persons  and  then  calculate  the  correlation 
coefficients  of  each  of  these  abilities  with  each  of  the  others. 
He  then  noticed  that  these  correlation  coefficients  had  a  certain 
ielationship  among  themselves,  which  he  called  a  hierarchial 
order.  By  this  he  means  that  if  the  coefficients  of  correlation 
of  a  number  of  mental  functions  are  arranged  in  a  descending 
cider  from  left  to  right  and  from  top  to  bottom  as  is  usualy 
done  in  a  correlation  table,  in  every  row  the  figures  will  be  in  a 
descending  order  as  they  are  in  the  top  row,  and  in  every  column 
the  figures  will  be  in  a  descending  order  as  they  are  in  the  left 
column.  This  also  means  that  in  any  table  of  correlations  as 
ordinarily  arranged,  every  column  will  have  a  perfect  correlation 
with  every  other  one.  Spearman  has  also  reduced  this  prin¬ 
ciple  to  the  following  exact  mathematical  equation : 

r  /r  =  r  /r  , 
ap  aq  bp  bq 

in  which  a,  b,  p  and  q  indicate  any  of  the  tests  and  r  is  the  cor- 
i  elation  between  them. 

It  seems  evident  that  the  presence  of  such  a  general  factor 
will  always  produce  this  hierarchy.  In  fact,  if  it  can  be  shown 
that  all  correlations  arrange  themselves  in  such  an  order,  it 
might  be  difficult  to  formulate  any  other  theory  to  account  for 
the  facts.  One  exception,  however,  is  enough  to  disprove  the 
theory,  since,  if  there  is  such  a  general  factor,  all  correlations 
must  take  this  hierarchical  form.  Thompson36  has  shown  that 
it  is  possible  with  dice  throws  to  get  a  set  of  correlation  coeffi¬ 
cients  in  excellent  hierarchical  order.  He  says  that  these  imita¬ 
tion  mental  tests  contain  no  general  factor.  Spearman,  on  the 
other  hand,  claims  that  Thompson  let  in  a  general  factor  at  the 

85  Spearman,  C.,  Manifold  Sub-Theories  of  the  “The  Two  Factors,” 
Psychol.  Rev.,  1920,  27 ,  159  ft. 

80  Thompson,  Godfrey  H.,  General  versus  Group  Factors  in  Mental  Activ¬ 
ities,  Psychol.  Rev.,  1920,  27 ,  173  ft. 


INTERRELA TION  OF  HIGHER  LEARNING  PROCESSES  61 


back  door.  It  seems  to  the  writer  that  Thompson  has  proved 
nothing  more  than  that  it  is  possible  occasionally  to  get  the  hier- 
archial  order  of  correlation  coefficients  when  there  is  no  general 
factor  present.  He  has  not  weakened  Spearman’s  argument  in 
the  least,  provided  Spearman  can  always  get  this  order.  Thomp¬ 
son  further  claims  in  this  same  article  that  the  hierarchical  order 
is  the  natural  relationship  among  correlation  coefficients.  The 
writer  is  unable  to  see,  however,  just  how  his  argument  bears 
upon  the  question.  He  is  willing,  of  course,  to  admit  that  this 
inability  may  be  due  to  his  lack  of  insight. 

Spearman,  in  order  to  prove  his  theory,  must  show  that  every 
group  of  correlation  coefficients  of  intellectual  functions  has, 
within  the  limits  of  experimental  accuracy,  this  hierarchical 
order.  Then  his  theory  will  hold  only  until  it  has  been  shown 
that  this  same  order  can  be  obtained  consistently  when  there  is 
no  common  factor  present.  The  data  of  this  investigation  and 
their  bearing  upon  the  question  are  here  presented. 

Table  XXXVI.  Showing  the  Correlation  Coefficients,  when  the  Tests 
are  Scored  in  the  Light  of  the  Criterion 


I 

3 

2 

5 

4 

I 

47 

33 

30 

26 

3 

47 

36 

18 

32 

2 

33 

36 

4i 

32 

5 

30 

18 

4i 

26 

4 

26 

32 

32 

26 

In  no  column,  except  the  first  where  it  was  deliberately  ar¬ 
ranged,  does  the  hierarchy  exist.  Spearman  would  probably  say 
that  the  mental  functions  here  tested  are  too  much  alike  for  the 
criterion  to  hold.  The  correlations  are  so  low,  however,  that 
this  claim  can  hardly  have  weight.  Our  findings  are  indeed 
adverse  to  the  Two  Factor  theory.  If  we  examine  the  correla¬ 
tions  and  partial  correlations  in  Table  XXVII,  it  will  be  evident 
that  no  factor  of  any  size  whatever  is  common  to  all  the  mental 


62 


B.  F.  H AUGHT 


functions  tested.  For  instance  the  correlation  of  tests  2  and  5 
is  .41.  When  the  elements  in  test  3,  common  to  2  and  5,  are 
removed,  the  correlation  is  still  .38.  This  indicates  that  there 
is  almost  nothing  common  to  the  three  tests.  This  same  con¬ 
clusion  can  be  deduced  from  other  cases  in  this  same  table.  The 
correlation  of  tests  2  and  3  with  the  common  elements  in  5  re¬ 
moved,  of  tests  3  and  4  with  the  common  elements  in  5  removed, 
of  tests  4  and  5  with  the  common  elements  in  3  removed,  leads 
to  the  conclusion  that  there  is  no  common  factor  large  enough 
to  account  for  all  the  correlations.  Table  XXXII  shows  the 
same  conditions.  The  correlation  of  tests  2  and  3  with  the 
common  elements  in  4  removed,  of  tests  2  and  5  with  the  com¬ 
mon  elements  in  4  removed,  of  tests  3  and  4  with  the  common 
elements  in  2  removed,  shows  that  there  are  no  elements  common 
to  all  the  tests  sufficient  to  account  for  all  the  correlations. 

Our  data  indicate  that  there  is  no  common  factor  of  any  size 
running  through  all  the  tests.  This  amounts  to  saying  that  there 
is  no  such  thing  as  general  intelligence.  What  then  is  the  nature 
of  intelligence?  One  other  theory  will  be  considered.  This 
theory  assumes  that  in  carrying  out  any  activity,  such  as  a  mental 
test,  a  number  of  factors  are  at  play.  Each  activity  involves  a 
specific  number  of  factors  combined  in  a  specific  way.  The 
specific  factors  combined  will  differ  with  different  individuals 
and  with  the  same  individual  at  different  times.  It  will  some¬ 
times  happen  that  a  number  of  elements  will  run  through  sev¬ 
eral  mental  activities.  In  this  case  there  may  be  said  to  be  an 
element  common  to  all  the  activities.  In  other  cases  there  will 
be  no  element  or  elements  common  to  more  than  two  or  three 
of  the  mental  functions.  For  instance,  tests  1  and  2  may  cor¬ 
relate  because  of  element  a,  tests  1  and  3  because  of  element  b, 
tests  2  and  3  because  of  element  c,  etc. 

This  theory  seems  to  be  in  harmony  with  the  data  of  this  in¬ 
vestigation.  According  to  the  Two  Factor  theory,  the  correla¬ 
tions  in  Table  XXXIII  show  that  test  3,  Rational  Learning 
(Modified),  must  have  more  of  the  general  factor  than  any  other 
test;  yet  when  the  elements  in  this  test  common  to  the  criterion 


INTERRELATION  OF  HIGHER  LEARNING  PROCESSES  63 


and  test  2,  to  the  criterion  and  test  4,  or  to  the  criterion  and  test  5, 
are  removed,  the  correlation  is  still  nearly  three  times  the  prob¬ 
able  error.  If  test  3  contains  more  of  the  general  factor  than 
any  other  test  and  all  correlation  is  due  to  this  factor,  then  it 
should  be  reduced  nearly  to  zero  when  the  common  elements  in 
this  factor  are  removed.  On  the  other  hand,  the  theory  of 
various  elements  variously  combined  can  easily  account  for  all 
correlations  and  partial  correlations.  That  is,  tests  1  and  2 
have  common  elements,  some  of  which  are  found  in  each  of 
the  other  three  tests  and  some  of  which  are  not  found  in  any  of 
the  other  three  tests.  The  same  conclusion  may  be  drawn  from 
tests  1  and  3  and  tests  1  and  5.  Probably  everything  common  to 
tests  1  and  4  is  found  in  tests  2  and  3  or  tests  3  and  5. 

If  we  now  turn  to  Table  XXVII,  it  is  evident  from  the  view¬ 
point  of  the  Two  Factor  theory  that  test  5  or  test  2  has  more 
of  the  general  factor  than  any  of  the  other  tests;  yet  when  the 
elements  in  5  common  to  3  and  4  are  removed,  the  correlation 
is  .28.  This  is  an  impossible  result  if  the  Two  Factor  theory  is 
true.  Table  XXXII  will  also  show  similar  conditions.  Test  2 
or  test  5  must  have  enough  of  the  general  factor  to  make  the 
correlation  of  these  two  tests  .44.  The  other  test  may  have  more 
of  this  factor,  but  cannot  have  less  if  Spearman’s  theory  is  true. 
Now  since  the  amount  of  the  general  factor  involved  in  either 
of  the  two  remaining  tests,  must  be  less  than  that  involved  in 
test  2  or  test  5,  the  correlation  of  these  tests,  3  and  4,  should  be 
reduced  to  zero,  when  the  common  elements  in  2  or  5  are  re¬ 
moved.  Yet  the  correlation  remains  .31  when  the  common 
elements  in  both  are  removed. 

These  data,  which  cannot  be  explained  at  all  by  the  Two  Fac¬ 
tor  theory,  are  easily  explained  by  the  theory  that  intelligence 
consists  of  a  large  number  of  factors  variously  grouped  and' 
combined.  Suppose  that  the  correlation  of  tests  2  and  3  in  table 
XXXII  is  due  to  elements  a,  b,  c,  d,  e,  f,  g,  h,  i,  and  j.  Now 
suppose  that  element  a  is  the  only  one  of  these  ten  that  is  found 
in  test  4,  and  that  elements  b,  c,  d,  and  e  are  the  only  ones  of  the 
ten  found  in  test  5.  When  the  element  a  is  removed  from  the 


64 


B.  F.  H AUGHT 


ten  common  ones,  the  correlation  is  reduced  from  .33  to  .29.  In 
like  manner,  when  the  elements  b,  c,  d,  and  e  are  removed,  the 
correlation  is  reduced  from  .33  to  .21.  When  the  elements  a,  b, 
c,  d,  and  e  are  removed,  the  correlation  is  reduced  from  .33  to 
.20.  Thus,  we  have  ten  elements  common  to  tests  2  and  3,  one 
element  common  to  tests  2,  3,  and  4,  four  elements  common  to 
tests  2,  3,  and  5.  This  analysis  is  not  literally  correct.  There  is 
undoubtedly  a  common  factor  of  very  small  importance  running 
through  all  four  tests.  This  is  evident  from  the  fact  that  r23.45 
is  not  much  less  than  r23.4  or  r23.5.  That  is,  most  of  the  elements 
in  test  4  common  to  tests  2  and  3  are  contained  in  the  elements 
m  test  5  common  to  tests  2  and  3.  An  examination  of  any  of 
the  correlations  and  the  accompanying  partial  correlations  will 
show  that  a  very  small  factor  runs  through  all  four  tests.  This 
factor,  however,  is  not  sufficient  to  account  for  the  correlations. 

It  seems  that  most  of  the  investigations,  when  interpreted  by 
Spearman,  are  in  harmony  with  the  Two  Factor  theory,  but 
when  interpreted  by  others,  are  adverse  to  this  theory  and  more 
in  harmony  with  the  other  theory  here  discussed.  Thorndike37 
has  recently  made  a  study,  using  the  Army  Tests  and  a  large 
number  of  subjects.  His  data  are  not  in  harmony  with  the  Two 
Factor  theory.  He  says  in  this  article : 

“We  have  considered  the  correlations  obtained  from  time  to 
time  in  various  studies  at  Teachers  College  from  the  point  of 
view  of  the  Spearman  theory,  and  have  in  general  not  been  able 
to  corroborate  it.  The  most  extensive  data  at  our  disposal 
(McCall,  T6)  seemed  decidedly  adverse.” 

Thorndike  in  this  same  article  further  says: 

“We  must,  it  appears,  turn  back  with  open  mind  to  the  details 
on  intercorrelations  and  experimental  analysis  to  work  out  the 
organization  of  intellect.  Especially  needed  seem  studies  of  the 
‘partial’  inter-correlations  with  one  after  another  of  the  factors 
equalized.” 

37Thorndike,  Edward  L.,  On  the  Organization  of  Intellect,  Psychol.  Rev., 
1921,  28 ,  141  ff. 


INTERRELATION  OF  HIGHER  LEARNING  PROCESSES  65 


Simpson38  discussed  general  intelligence  and  the  bearings  of 
his  study  upon  the  Two  Factor  theory.  He  says: 

“We  find  justification  for  the  common  assumption  that  there 
is  close  inter-relation  among  certain  mental  abilities,  and  cotv 
sequently  a  something  that  may  be  called  ‘general  mental  ability' 
or  ‘general  intelligence’ ;  and  that  on  the  other  hand  certain 
capacities  are  relatively  specialized,  and  do  not  imply  other 
abilities  except  to  a  very  limited  extent.” 

He  says  again:  “We  find  no  justification  for  the  view  that 
‘general  intelligence'  is  to  be  explained  on  the  basis  of  a  hier¬ 
archy  of  mental  functions,  the  amount  of  correlation  in  each 
case  being  due  to  the  degree  of  connection  with  a  common  cen¬ 
tral  factor." 

Peterson39  makes  the  following  statement  as  to  the  nature  of 
general  intelligence:  “General  intelligence,  if  it  is  a  reality  at 
all,  is  probably  not  a  separate  constant  factor,  but  a  composite 
of  many  different  abilities,  and  probably  means  different  things 
in  unlike  situations,  as  different  abilities  are  stressed.  Such 
factors  as  energy  and  perseverance,  degree  of  disturbance  by 
emotions  and  self-consciousness,  and  many  others  that  play  their 
role  in  one’s  success  in  life,  have  not  yet  been  successfully  brought 
into  the  field  of  measurement  by  tests,  especially  by  group  tests." 

XI.  Summary  and  Conclusions 

A.  Method.  The  essential  features  of  the  method  used  in 
this  investigation  are: 

( 1 )  Four  tests  of  the  problem  solving  or  rational  learning 
type  are  used.  Two  of  these  tests  have  five  kinds  of  data — time, 
repetitions,  and  three  kinds  of  errors.  One  has  three  kinds  of 
data — time,  attempts  and  solutions.  One  has  two  kinds  of  data — 
time  and  number  of  trials.  A  criterion,  the  Stanford  Revision  of 
the  Binet-Simon  tests,  is  used  in  finding  the  best  method  of  scor- 

38  Simpson,  Benj.  R.,  Correlations  of  Mental  Abilities,  Teachers’  College 
Contributions  to  Education ,  1912  (No.  53). 

39  Peterson,  Joseph,  Intelligence  and  Its  Measurement,  J.  of  Educ.  Psychol , 
1921,  12 ,  198#. 


66 


B.  F.  H AUGHT 


ing  or  combining  the  different  kinds  of  data  and  in  analyzing 
the  tests. 

(2)  The  raw  scores  in  the  criterion  and  in  each  factor  of 
each  test,  and  the  final  scores  are  transmuted  into  percentiles. 
This  has  been  found  very  helpful  in  calculating  correlations. 
For  instance,  all  standard  deviations  as  well  as  all  the  means  are 
made  approximately  equal.  The  analysis  of  the  curves  through 
the  means  of  the  rows  and  columns  is  also  simpler  when  the 
standard  deviations  are  equal. 

(3)  Every  factor  in  a  test  is  correlated  with  the  criterion  and 
with  every  other  factor.  Then  a  complete  set  of  partial  cor¬ 
relations  is  worked  out.  This  makes  it  possible  to  determine 
which  factors  must  be  used  in  scoring  in  order  not  to  discard 
any  elements  in  common  with  the  criterion.  For  instance,  it  was 
found  in  Rational  Learning  that  repetitions  and  perseverative 
errors  contain  everything  in  all  the  factors  in  common  with  the 
criterion.  That  is,  everything  in  the  other  three  factors  is  a 
duplication  of  these  common  elements  in  repetitions  and  per¬ 
severative  errors. 

(4)  To  determine  the  best  combination  of  the  factors  that 
need  to  be  retained,  formula  (2)  is  used.  Formula  (3)  is  then 
used  to  determine  what  this  correlation  is.  As  a  check  on  the 
work,  formula  ( 1 )  is  used.  This  gives  the  highest  possible 
correlation  of  all  the  factors  with  the  criterion.  If  this  result 
agrees  closely  with  that  obtained  from  formula  (2),  it  is  evi¬ 
dence  that  the  analysis  and  work  are  correct.  It  so  happened 
that  not  more  than  two  factors  needed  to  be  combined  in  any 
of  the  tests;  but  if  it  had  been  necessary  to  combine  three  or 
more  factors,  two  would  have  been  combined  in  the  best  way 
and  then  this  result  with  the  third  factor.  The  writer  has  com¬ 
bined  as  many  as  five  factors  in  this  way  and  found  it  very  satis¬ 
factory. 

(5)  For  every  correlation,  Blakeman’s  criterion  for  linearity 
is  applied.  If  non-linearity  exists  according  to  this  criterion, 
the  actual  curves  of  the  means  of  the  rows  and  columns  are  con¬ 
structed.  The  writer  regards  the  correlation-ratio  and  the  Blake- 


INTERRELATION  OF  HIGHER  LEARNING  PROCESSES  67 


man  criterion  of  very  little  value  unless  the  number  of  cases  is 
large  enough  to  eliminate  most  of  the  fluctuations  in  the  curves 
through  the  means  of  the  rows  and  columns.  These  fluctuations 
are  often  sufficient  to  produce  a  high  correlation-ratio  when 
there  is  no  correlation,  and,  of  course,  non-linearity  is  indicated 
when  the  criterion  is  applied.  The  actual  curves  through  the 
means  of  the  rows  and  columns  are  of  more  significance,  since 
it  is  possible  to  determine  the  general  direction  of  such  curves  in 
making  analyses. 

(6)  The  final  scores  of  each  test  are  analyzed  by  comparing 
them  with  the  criterion  through  the  use  of  partial  correlations 
and  multiple  correlation.  It  does  not  seem  possible  to  do  much 
with  partial  correlations  in  analysis  unless  a  criterion  is  used. 

(7)  The  final  scores  as  obtained  in  the  light  of  the  criterion 
are  correlated  with  each  other  and  partial  correlations  worked 
out.  In  comparing  the  tests  with  each  other,  the  multiple  cor¬ 
relation  method  is  found  very  valuable.  Especially  is  this  the 
case  in  determining  how  much  each  test  has  in  common  with  all 
the  others. 

(8)  As  a  final  step  in  the  technique,  the  tests  are  scored  by 
combining  all  the  factors  in  a  test  equally.  This  was  thought 
best,  since  there  was  a  possibility  of  accentuating  certain  elements 
in  the  tests  by  scoring  them  in  the  light  of  the  criterion. 

B.  Results.  The  results  indicated  by  the  data  are  as  follows : 

(1)  In  scoring  Rational  Learning  in  the  light  of  the  criterion, 
repetitions  and  perseverative  errors  are  the  significant  factors. 
Time,  unclassified  errors,  and  logical  errors  only  duplicate  the 
elements  in  these  two  factors.  Time  and  unclassified  errors  are 
the  significant  factors  in  Rational  Learning  (Modified)  ;  the 
other  three  factors  may  be  discarded.  The  number  of  solutions 
is  the  significant  factor  in  the  Checker  Puzzle.  Time  and  num¬ 
ber  of  attempts  add  nothing.  In  the  Tait  Labyrinth  Puzzle  the 
number  of  trials  is  the  significant  factor.  Time  is  unessential. 
It  might  be  interesting  to  note  here  that  in  three  of  the  four  tests, 
time  is  an  unessential  factor.  This  does  not  mean,  however, 
that  the  same  results  would  have  been  obtained  if  the  subject 


68 


B.  F.  H AUGHT 


had  been  told  that  time  was  not  being  considered.  The  cor¬ 
relations  would  probably  have  been  very  different.  Time  is 
probably  not  important  in  the  Checker  Puzzle  and  the  Tait  Laby¬ 
rinth  Puzzle.  In  Rational  Learning  the  subject  is  controlled 
somewhat  by  the  experimenter  but  in  Rational  Learning 
(Modified)  he  is  free  to  go  as  fast  as  he  wishes.  This  probably 
accounts  for  the  difference  in  the  value  of  the  time  factor  in  the 
two  tests.  In  Rational  Learning  (Modified)  the  space  percep¬ 
tion  makes  it  easier  to  avoid  perseverative  errors,  and  for  that 
reason  this  factor  becomes  unessential.  It  is  thought  best  to 
make  no  comparison  of  the  difficulty  of  the  two  rational  learn¬ 
ing  tests,  since  each  subject  had  already  taken  Rational  Learning 
(Modified),  when  he  took  Rational  Learning.  The  similarity 
was  usually  recognized  at  once.  It  was  not  uncommon  to  have 
the  subject  say  while  he  was  reading  the  directions  for  Rational 
Learning,  “This  is  just  like  that  bell-ringing  thing.” 

(2)  Rational  Learning  and  Rational  Learning  (Modified) 
seem  to  test  or  measure  mental  functions  not  detected  by  the 
intelligence  tests.  These  may  be  summarized  as  follows :  first, 
the  ability  to  attack  and  solve  a  problem  without  getting  con¬ 
fused;  second,  the  ability  to  give  attention  longer  than  that 
usually  required  in  mental  tests;  third,  the  type  of  attack  made 
by  the  subject;  and  fourth,  the  speed  of  the  subject.  The  ob¬ 
jective  data  do  not  reveal  any  mental  functions  tested  by  the 
Checker  Puzzle  and  the  Tait  Labyrinth  Puzzle  over  and  above 
those  tested  by  the  criterion. 

( 3 )  Rational  Learning  (  Modified )  correlates  considerably  higher 
with  the  criterion  than  does  any  of  the  other  tests.  This  may 
be  partly  due  to  the  fact  that  this  test  was  given  first.  The 
Checker  Puzzle  has  the  lowest  correlation  with  the  criterion. 
Rational  Learning  (Modified)  has  elements  in  common  with  the 
criterion  that  are  not  found  in  the  other  three  tests.  The  same 
is  probably  true  of  the  Tait  Labyrinth  Puzle,  but  to  a  less  ex¬ 
tent.  Rational  Learning  and  the  Checker  Puzzle  have  nothing 
in  common  with  the  criterion  that  is  not  found  in  the  other  tests. 

(4)  When  the  tests  are  scored  in  the  light  of  the  criterion, 


INTERRELATION  OF  HIGHER  LEARNING  PROCESSES  69 


every  correlation  indicates  something  in  common  between  the 
two  tests  correlated.  The  correlations  of  the  second  order  also 
indicate  that  each  pair  of  tests,  except  3  and  5,  have  something 
in  common  that  is  not  contained  in  the  other  tests.  The  factor 
running  through  all  four  tests  is  almost  zero.  Multiple  correla¬ 
tion  shows  that  each  test  has  much  that  is  not  contained  in  the 
other  three  tests.  The  Checker  Puzzle  has  most,  the  Tait  Laby¬ 
rinth  comes  second  and  Rational  Learning  has  least.  The  dif¬ 
ferences  are  so  small  that  they  are  probably  not  significant. 

(5)  When  the  tests  are  scored  by  combining  all  the  factors 
in  a  test  equally,  the  same  general  results  are  obtained  as  in  the 
other  method  of  scoring.  There  are  some  differences,  however, 
in  specific  correlations.  These  are  evident  when  tables  XXVI 
and  XXXII  are  examined.  The  correlations  of  test  2  with  test 
3  and  test  5  are  not  changed  much,  but  the  correlation  of  test  2 
with  test  4  is  reduced  about  half.  The  correlation  of  test  3  with 
test  4  is  not  changed  much,  but  that  of  test  3  with  test  5  is  about 
doubled.  The  relations  of  test  4  with  test  5  remain  exactly  the 
same.  The  multiple  correlations  show  very  little  change  in 
general  by  the  two  methods  of  scoring. 

(6)  There  is  nothing  in  the  data  of  this  investigation  to 
justify  the  Two  Factor  theory  of  intelligence.  In  fact,  every¬ 
thing  is  adverse  to  this  theory.  If  the  testing  and  the  calcula¬ 
tions  are  absolutely  free  from  errors,  the  results  obtained  are 
impossible  on  the  basis  of  the  Two  Factor  theory.  The  correla¬ 
tions  and  partial  correlations  can  be  accounted  for,  however,  by 
the  theory  that  intelligence  consists  of  various  factors  variously 
grouped  for  different  situations. 


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